메뉴 건너뛰기




Volumn 16, Issue 3, 2006, Pages 431-453

Sobolev space estimates and symbolic calculus for bilinear pseudodifferential operators

Author keywords

asymptotic expansion; Bilinear pseudodifferential operators; composition; elementary symbols; Littlewood Paley theory

Indexed keywords


EID: 33748293142     PISSN: 10506926     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02922061     Document Type: Article
Times cited : (35)

References (36)
  • 1
    • 24444472582 scopus 로고    scopus 로고
    • Bilinear singular integrals and pseudodifferential operators
    • University of Kansas Lawrence
    • Bényi, Á. Bilinear singular integrals and pseudodifferential operators, PhD Thesis, University of Kansas, Lawrence, (2002).
    • (2002) PhD Thesis
    • Bényi, Á.1
  • 2
    • 18244422210 scopus 로고    scopus 로고
    • Bilinear pseudodifferential operators with forbidden symbols on Lipschitz and Besov spaces
    • 10.1016/S0022-247X(03)00245-2 1996120 1037.35113
    • Ä. Bényi 2003 Bilinear pseudodifferential operators with forbidden symbols on Lipschitz and Besov spaces J. Math. Anal. Appl. 284 97 103 10.1016/S0022-247X(03)00245-2 1996120 1037.35113
    • (2003) J. Math. Anal. Appl. , vol.284 , pp. 97-103
    • Bényi, Ä.1
  • 3
    • 33645855163 scopus 로고    scopus 로고
    • Modulation spaces and a class of bounded multilinear pseudodifferential operators
    • to appear
    • Bényi, Á.; Gröchenig, K.; Heil, C.; and Okoudjou, K. Modulation spaces and a class of bounded multilinear pseudodifferential operators,J. Operator Theory to appear.
    • J. Operator Theory
    • Bényi, Á.1    Gröchenig, K.2    Heil, C.3    Okoudjou, K.4
  • 4
    • 0037704914 scopus 로고    scopus 로고
    • Symbolic calculus and the transposes of bilinear pseudodifferential operators
    • 10.1081/PDE-120021190 1986065 1103.35370
    • Á. Bényi R. H. Torres 2003 Symbolic calculus and the transposes of bilinear pseudodifferential operators Comm. Partial Differential Equations 28 1161 1181 10.1081/PDE-120021190 1986065 1103.35370
    • (2003) Comm. Partial Differential Equations , vol.28 , pp. 1161-1181
    • Bényi, Á.1    Torres, R.H.2
  • 5
    • 2442515444 scopus 로고    scopus 로고
    • Almost orthogonality and a class of bounded bilinear pseudodifferential operators
    • 2046194 1067.47062
    • Á. Bényi R. H. Torres 2004 Almost orthogonality and a class of bounded bilinear pseudodifferential operators Math. Res. Lett. 11 1 11 2046194 1067.47062
    • (2004) Math. Res. Lett. , vol.11 , pp. 1-11
    • Bényi, Á.1    Torres, R.H.2
  • 6
    • 84963458222 scopus 로고
    • p-estimates for certain nonregular pseudo-differential operators
    • 10.1080/03605308208820244 673825 0499.35097
    • p-estimates for certain nonregular pseudo-differential operators Comm. Partial Differential Equations 7 1023 1033 10.1080/03605308208820244 673825 0499.35097
    • (1982) Comm. Partial Differential Equations , vol.7 , pp. 1023-1033
    • Bourdaud, G.1
  • 7
    • 0742288808 scopus 로고    scopus 로고
    • P,p > 2n
    • 10.1007/s00041-003-0902-3 2026763 1051.35105
    • P,p > 2n J. Fourier Anal. Appl. 9 6 563 574 10.1007/s00041-003-0902-3 2026763 1051.35105
    • (2003) J. Fourier Anal. Appl. , vol.9 , Issue.6 , pp. 563-574
    • Brown, R.M.1    Torres, R.H.2
  • 8
    • 0036115549 scopus 로고    scopus 로고
    • On the well-posedness of the Euler equations in the Triebel-Lizorkin spaces
    • 10.1002/cpa.10029 1880646 1025.35016
    • D. Chae 2002 On the well-posedness of the Euler equations in the Triebel-Lizorkin spaces Comm. Pure Appl. Math. 55 654 678 10.1002/cpa.10029 1880646 1025.35016
    • (2002) Comm. Pure Appl. Math. , vol.55 , pp. 654-678
    • Chae, D.1
  • 9
    • 0002645561 scopus 로고
    • Dispersion of small amplitude solutions of the generalized Korteweg-de Vries equation
    • 10.1016/0022-1236(91)90103-C 1124294 0743.35067
    • F. M. Christ M. I. Weinstein 1991 Dispersion of small amplitude solutions of the generalized Korteweg-de Vries equation J. Func. Anal. 100 87 109 10.1016/0022-1236(91)90103-C 1124294 0743.35067
    • (1991) J. Func. Anal. , vol.100 , pp. 87-109
    • Christ, F.M.1    Weinstein, M.I.2
  • 10
    • 0002540644 scopus 로고
    • Hardy space estimates for multilinear operators, i
    • 1178448 0785.47025
    • R. R. Coifman L. Grafakos 1992 Hardy space estimates for multilinear operators, I Rev. Mat. Iberoamericana 8 45 67 1178448 0785.47025
    • (1992) Rev. Mat. Iberoamericana , vol.8 , pp. 45-67
    • Coifman, R.R.1    Grafakos, L.2
  • 12
    • 84966238915 scopus 로고
    • On commutators of singular integrals and bilinear singular integrals
    • 10.2307/1998628 380244 0324.44005
    • R. R. Coifman Y. Meyer 1975 On commutators of singular integrals and bilinear singular integrals Trans. Amer. Math. Soc. 212 315 331 10.2307/1998628 380244 0324.44005
    • (1975) Trans. Amer. Math. Soc. , vol.212 , pp. 315-331
    • Coifman, R.R.1    Meyer, Y.2
  • 13
    • 0001072134 scopus 로고
    • Commutateurs d'intégrales singulièrs et opérateurs multilinéaires
    • 511821 0368.47031
    • R. R. Coifman Y. Meyer 1978 Commutateurs d'intégrales singulièrs et opérateurs multilinéaires Ann. Inst. Fourier (Grenoble) 28 177 202 511821 0368.47031
    • (1978) Ann. Inst. Fourier (Grenoble) , vol.28 , pp. 177-202
    • Coifman, R.R.1    Meyer, Y.2
  • 14
    • 0001923237 scopus 로고
    • Au-delà des opérateurs pseudo-diffeŕentiels
    • Société Math. de France
    • Coifman, R.R. and Meyer, Y. Au-delà des opérateurs pseudo-diffeŕentiels,Astérisque 57, Société Math. de France, (1978).
    • (1978) Astérisque , pp. 57
    • Coifman, R.R.1    Meyer, Y.2
  • 15
    • 22644452497 scopus 로고    scopus 로고
    • Hardy spaces and a Walsh model for bilinear cone operators
    • 10.1090/S0002-9947-99-02490-3 1665331 0919.42009
    • J. Gilbert A. Nahmod 1999 Hardy spaces and a Walsh model for bilinear cone operators Trans. Amer. Math. Soc. 351 3267 3300 10.1090/S0002-9947-99- 02490-3 1665331 0919.42009
    • (1999) Trans. Amer. Math. Soc. , vol.351 , pp. 3267-3300
    • Gilbert, J.1    Nahmod, A.2
  • 16
    • 0034348694 scopus 로고    scopus 로고
    • Boundedness of bilinear operators with nonsmooth symbols
    • 1809300 0987.42017
    • J. Gilbert A. Nahmod 2000 Boundedness of bilinear operators with nonsmooth symbols Math. Res. Lett. 7 767 778 1809300 0987.42017
    • (2000) Math. Res. Lett. , vol.7 , pp. 767-778
    • Gilbert, J.1    Nahmod, A.2
  • 17
    • 0345775324 scopus 로고    scopus 로고
    • Bilinear operators with nonsmooth symbols. i
    • 10.1007/BF02511220 1845098 0994.42014
    • J. Gilbert A. Nahmod 2001 Bilinear operators with nonsmooth symbols. I J. Fourier Anal. Appl. 7 5 435 467 10.1007/BF02511220 1845098 0994.42014
    • (2001) J. Fourier Anal. Appl. , vol.7 , Issue.5 , pp. 435-467
    • Gilbert, J.1    Nahmod, A.2
  • 18
    • 0035998668 scopus 로고    scopus 로고
    • p-boundedness of time-frequency paraproducts, II
    • 10.1007/s00041-002-0006-5 1891727 1028.42013
    • p-boundedness of time-frequency paraproducts, II J. Fourier Anal. Appl. 8 2 109 172 10.1007/s00041-002-0006-5 1891727 1028.42013
    • (2002) J. Fourier Anal. Appl. , vol.8 , Issue.2 , pp. 109-172
    • Gilbert, J.1    Nahmod, A.2
  • 19
    • 0002540644 scopus 로고
    • Hardy space estimates for multilinear operators, II
    • 1178449 0785.47026
    • L. Grafakos 1992 Hardy space estimates for multilinear operators, II Rev. Mat. Iberoamericana 8 69 92 1178449 0785.47026
    • (1992) Rev. Mat. Iberoamericana , vol.8 , pp. 69-92
    • Grafakos, L.1
  • 20
    • 0035993969 scopus 로고    scopus 로고
    • Discrete decompositions for bilinear operators and almost diagonal conditions
    • 10.1090/S0002-9947-01-02912-9 1867376 0988.42013
    • L. Grafakos R. H. Torres 2002 Discrete decompositions for bilinear operators and almost diagonal conditions Trans. Amer. Math. Soc. 354 1153 1176 10.1090/S0002-9947-01-02912-9 1867376 0988.42013
    • (2002) Trans. Amer. Math. Soc. , vol.354 , pp. 1153-1176
    • Grafakos, L.1    Torres, R.H.2
  • 21
    • 0037081869 scopus 로고    scopus 로고
    • Multilinear Calderón-Zygmund theory
    • 10.1006/aima.2001.2028 1880324 1032.42020
    • L. Grafakos R. H. Torres 2002 Multilinear Calderón-Zygmund theory Adv. Math. 165 124 164 10.1006/aima.2001.2028 1880324 1032.42020
    • (2002) Adv. Math. , vol.165 , pp. 124-164
    • Grafakos, L.1    Torres, R.H.2
  • 23
    • 84981750225 scopus 로고
    • Pseudo-differential operators
    • 10.1002/cpa.3160180307 180740 0125.33401
    • L. Hörmander 1965 Pseudo-differential operators Comm. Pure Appl. Math. 18 501 517 10.1002/cpa.3160180307 180740 0125.33401
    • (1965) Comm. Pure Appl. Math. , vol.18 , pp. 501-517
    • Hörmander, L.1
  • 24
    • 84990617895 scopus 로고
    • Commutator estimates and the Euler and Navier-Stokes equations
    • 10.1002/cpa.3160410704 951744 0671.35066
    • T. Kato G. Ponce 1988 Commutator estimates and the Euler and Navier-Stokes equations Comm. Pure Appl. Math. 41 891 907 10.1002/cpa.3160410704 951744 0671.35066
    • (1988) Comm. Pure Appl. Math. , vol.41 , pp. 891-907
    • Kato, T.1    Ponce, G.2
  • 25
    • 84990553608 scopus 로고
    • Well-posedness and scattering results for the generalized Korteweg-de Vries equation via the contraction principle
    • 10.1002/cpa.3160460405 1211741 0808.35128
    • C. Kenig G. Ponce L. Vega 1993 Well-posedness and scattering results for the generalized Korteweg-de Vries equation via the contraction principle Comm. Pure Appl. Math. 46 527 620 10.1002/cpa.3160460405 1211741 0808.35128
    • (1993) Comm. Pure Appl. Math. , vol.46 , pp. 527-620
    • Kenig, C.1    Ponce, G.2    Vega, L.3
  • 26
    • 0033243373 scopus 로고    scopus 로고
    • Multilinear estimates and fractional integration
    • 1682725 0952.42005
    • C. Kenig E. Stein 1999 Multilinear estimates and fractional integration Math. Res. Lett. 6 1 15 1682725 0952.42005
    • (1999) Math. Res. Lett. , vol.6 , pp. 1-15
    • Kenig, C.1    Stein, E.2
  • 27
    • 84981761181 scopus 로고
    • An algebra of pseudodifferential operators
    • 10.1002/cpa.3160180121 176362 0171.35101
    • J. J. Kohn L. Nirenberg 1965 An algebra of pseudodifferential operators Comm. Pure Appl. Math. 18 269 305 10.1002/cpa.3160180121 176362 0171.35101
    • (1965) Comm. Pure Appl. Math. , vol.18 , pp. 269-305
    • Kohn, J.J.1    Nirenberg, L.2
  • 28
    • 0001283252 scopus 로고    scopus 로고
    • p-bounds for the bilinear Hilbert transform, 2

    • 10.2307/2952458 1491450 0914.46034
    • p-bounds for the bilinear Hilbert transform, 2

    • (1997) Ann. of Math. (2) , vol.146 , pp. 693-724
    • Lacey, M.1    Thiele, C.2
  • 29
    • 0033416840 scopus 로고    scopus 로고
    • Calderón's conjecture
    • 10.2307/120971 1689336 0934.42012
    • M. Lacey C. Thiele 1999 Calderón's conjecture Ann. of Math. (2) 149 475 496 10.2307/120971 1689336 0934.42012
    • (1999) Ann. of Math. (2) , vol.149 , pp. 475-496
    • Lacey, M.1    Thiele, C.2
  • 31
    • 18444396627 scopus 로고    scopus 로고
    • Bi-parameter paraproducts
    • 10.1007/BF02392566 2134868 1087.42016
    • C. Muscalu J. Pipher T. Tao C. Thiele 2004 Bi-parameter paraproducts Acta Math. 193 269 296 10.1007/BF02392566 2134868 1087.42016
    • (2004) Acta Math. , vol.193 , pp. 269-296
    • Muscalu, C.1    Pipher, J.2    Tao, T.3    Thiele, C.4
  • 32
    • 0036004363 scopus 로고    scopus 로고
    • Multilinear operators given by singular multipliers
    • 10.1090/S0894-0347-01-00379-4 1887641 0994.42015
    • C. Muscalu T. Tao C. Thiele 2002 Multilinear operators given by singular multipliers J. Amer. Math. Soc. 15 469 496 10.1090/S0894-0347-01-00379-4 1887641 0994.42015
    • (2002) J. Amer. Math. Soc. , vol.15 , pp. 469-496
    • Muscalu, C.1    Tao, T.2    Thiele, C.3
  • 33
    • 2442713801 scopus 로고    scopus 로고
    • Embeddings of some classical Banach spaces into modulation spaces
    • 10.1090/S0002-9939-04-07401-5 2051124 1044.46030
    • K. Okoudjou 2004 Embeddings of some classical Banach spaces into modulation spaces Proc. Amer. Math. Soc. 132 1639 1647 10.1090/S0002-9939-04- 07401-5 2051124 1044.46030
    • (2004) Proc. Amer. Math. Soc. , vol.132 , pp. 1639-1647
    • Okoudjou, K.1
  • 36
    • 0003292824 scopus 로고
    • Special trigonometric series in k-dimensions
    • Wainger, S. Special trigonometric series in k-dimensions,Mem. Amer. Math. Soc. 59, (1965).
    • (1965) Mem. Amer. Math. Soc. , vol.59
    • Wainger, S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.