메뉴 건너뛰기




Volumn 47, Issue 1, 1998, Pages 123-151

Poincaré inequalities, isoperimetric estimates, and representation formulas on product spaces

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0039657240     PISSN: 00222518     EISSN: None     Source Type: Journal    
DOI: 10.1512/iumj.1998.47.1494     Document Type: Article
Times cited : (21)

References (29)
  • 1
    • 0001793269 scopus 로고
    • Remarks on Sobolev imbedding inequalities
    • Springer-Verlag, New York
    • B. BOJARSKI, Remarks on Sobolev Imbedding Inequalities, Lecture Notes in Math., 1351, Springer-Verlag, New York, 1989, pp. 52-68.
    • (1989) Lecture Notes in Math. , vol.1351 , pp. 52-68
    • Bojarski, B.1
  • 2
    • 0001651403 scopus 로고
    • Inequalities for the maximal function relative to a metric
    • A. P. CALDERON, Inequalities for the maximal function relative to a metric, Studia Math. 57 (1976), 297-306.
    • (1976) Studia Math. , vol.57 , pp. 297-306
    • Calderon, A.P.1
  • 3
    • 0031285615 scopus 로고    scopus 로고
    • Subelliptic mollifiers and a basic pointwise estimate of poincaré type
    • L. CAPOGNA, D. DANIELLI, AND N. GAROFALO, Subelliptic mollifiers and a basic pointwise estimate of Poincaré type, Math. Zeit. 226 (1997), 147-154.
    • (1997) Math. Zeit. , vol.226 , pp. 147-154
    • Capogna, L.1    Danielli, D.2    Garofalo, N.3
  • 4
    • 0001580578 scopus 로고
    • Weighted Poincaré and Sobolev inequalities and estimates for the Peano maximal function
    • S. CHANILLO AND R. L. WHEEDEN, Weighted Poincaré and Sobolev inequalities and estimates for the Peano maximal function, Amer. J. Math. 107 (1985), 1191-1226.
    • (1985) Amer. J. Math. , vol.107 , pp. 1191-1226
    • Chanillo, S.1    Wheeden, R.L.2
  • 5
    • 84972493816 scopus 로고
    • Weighted Sobolev inequalities of mixed norm
    • S.-K. CHUA, Weighted Sobolev inequalities of mixed norm, Real Analysis Exchange 21 (1995), 555-571.
    • (1995) Real Analysis Exchange , vol.21 , pp. 555-571
    • Chua, S.-K.1
  • 6
    • 0003232322 scopus 로고
    • Analyse harmonique non-commutative sur certains espaces homogènes
    • Springer Verlag, New York
    • R. R. COIFMAN AND G. WEISS, Analyse Harmonique Non-commutative sur Certains Espaces Homogènes, Lecture Notes in Math., 242, Springer Verlag, New York, 1971.
    • (1971) Lecture Notes in Math. , vol.242
    • Coifman, R.R.1    Weiss, G.2
  • 7
    • 0001229163 scopus 로고
    • Subelliptic eigenvalue estimates
    • Chicago, (W. Beckner et. al., eds.), Wadsworth
    • C. FEFFERMAN AND D. H. PHONG, Subelliptic eigenvalue estimates, Conference on Harmonic Analysis, Chicago, 1980 (W. Beckner et. al., eds.), Wadsworth, 1981, pp. 590-606.
    • (1980) Conference on Harmonic Analysis , pp. 590-606
    • Fefferman, C.1    Phong, D.H.2
  • 8
    • 84966205984 scopus 로고
    • Weighted Sobolev-Poincaré inequalities and pointwise estimates for a class of degenerate elliptic equations
    • B. FRANCHI, Weighted Sobolev-Poincaré inequalities and pointwise estimates for a class of degenerate elliptic equations, Trans. Amer. Math. Soc. 327 (1991), 125-158.
    • (1991) Trans. Amer. Math. Soc. , vol.327 , pp. 125-158
    • Franchi, B.1
  • 9
    • 0001010690 scopus 로고
    • Sobolev and isoperimetnc inequalities for degenerate metrics
    • B. FRANCHI, S. GALLOT AND R. L. WHEEDEN, Sobolev and isoperimetnc inequalities for degenerate metrics, Math. Ann. 300 (1994), 557-571.
    • (1994) Math. Ann. , vol.300 , pp. 557-571
    • Franchi, B.1    Gallot, S.2    Wheeden, R.L.3
  • 10
    • 0001077590 scopus 로고
    • Weighted Sobolev-Poincaré inequalities for Grushin type operators
    • B. FRANCHI, C. E. GUTIERREZ AND R.L. WHEEDEN, Weighted Sobolev-Poincaré inequalities for Grushin type operators, Comm. P.D.E. 19 (1994), 523-604.
    • (1994) Comm. P.D.E. , vol.19 , pp. 523-604
    • Franchi, B.1    Gutierrez, C.E.2    Wheeden, R.L.3
  • 11
    • 0000541936 scopus 로고
    • Hölder regularity for a class of linear non uniformly elliptic operators with measurable coefficients
    • B. FRANCHI AND E. LANCONELLI, Hölder regularity for a class of linear non uniformly elliptic operators with measurable coefficients, Ann. Scuola Norm. Sup. Pisa (IV) 10 (1983), 523-541.
    • (1983) Ann. Scuola Norm. Sup. Pisa (IV) , vol.10 , pp. 523-541
    • Franchi, B.1    Lanconelli, E.2
  • 12
    • 0000502355 scopus 로고
    • Representation formulas and weighted Poincaré inequalities for Hörmander vector fields
    • Grenoble
    • B. FRANCHI, G. LU AND R. L. WHEEDEN, Representation formulas and weighted Poincaré inequalities for Hörmander vector fields, Ann. Inst. Fourier, Grenoble 45 (1995), 577-604.
    • (1995) Ann. Inst. Fourier , vol.45 , pp. 577-604
    • Franchi, B.1    Lu, G.2    Wheeden, R.L.3
  • 13
    • 0344454983 scopus 로고    scopus 로고
    • A relationship between Poincaré-type inequalities and representation formulas in spaces of homogeneous type
    • B. FRANCHI, G. LU, R. L. WHEEDEN, A relationship between Poincaré-type inequalities and representation formulas in spaces of homogeneous type, Intern. Math. Res. Notices (1996), 1-14.
    • (1996) Intern. Math. Res. Notices , pp. 1-14
    • Franchi, B.1    Lu, G.2    Wheeden, R.L.3
  • 14
    • 84875554440 scopus 로고    scopus 로고
    • Self-improving properties of John-Nirenberg and Poincaré inequalities on spaces cf homogeneous type
    • to appear
    • B. FRANCHI, C. PEREZ AND R. L. WHEEDEN, Self-improving properties of John-Nirenberg and Poincaré inequalities on spaces cf homogeneous type, J. Funct. Anal. (to appear).
    • J. Funct. Anal.
    • Franchi, B.1    Perez, C.2    Wheeden, R.L.3
  • 15
    • 0001740045 scopus 로고
    • Pointwise estimates for a class of strongly degenerate elliptic operators: A geometrical approach
    • B. FRANCHI AND R. SERAPIONI, Pointwise estimates for a class of strongly degenerate elliptic operators: a geometrical approach, Ann. Scuola Norm. Sup. Pisa 14 (1987 (IV)), 527-568.
    • (1987) Ann. Scuola Norm. Sup. Pisa , vol.14 , pp. 527-568
    • Franchi, B.1    Serapioni, R.2
  • 16
    • 0041653105 scopus 로고    scopus 로고
    • Some remarks about Pomcaré type inequalities and representation formulas in metric, spaces of homogeneous type
    • to appear
    • B. FRANCHI AND R. L. WHEEDEN, Some remarks about Pomcaré type inequalities and representation formulas in metric, spaces of homogeneous type, J. Inequalities and Applications (to appear).
    • J. Inequalities and Applications
    • Franchi, B.1    Wheeden, R.L.2
  • 17
    • 0030488404 scopus 로고    scopus 로고
    • Isoperimetric and sobolev inequalities for Carnot-Carathéodory spaces and the existence of minimal surfaces
    • N. GAROFALO AND D. M. NHIEU, Isoperimetric and Sobolev inequalities for Carnot-Carathéodory spaces and the existence of minimal surfaces, CPAM 49 (1996), 1081-1144.
    • (1996) CPAM , vol.49 , pp. 1081-1144
    • Garofalo, N.1    Nhieu, D.M.2
  • 19
    • 15244346736 scopus 로고
    • Hypoelliptic second order differential equations
    • L. HÖRMANDER, Hypoelliptic second order differential equations, Acta Math. 119 (1967), 147-171.
    • (1967) Acta Math. , vol.119 , pp. 147-171
    • Hörmander, L.1
  • 20
    • 84972555264 scopus 로고
    • The Poincaré inequality for vector fields satisfying Hörmander's condition
    • D. JERISON, The Poincaré inequality for vector fields satisfying Hörmander's condition, Duke Math. J. 53 (1986), 503-523.
    • (1986) Duke Math. J. , vol.53 , pp. 503-523
    • Jerison, D.1
  • 21
    • 84875554620 scopus 로고
    • Subelliptic second order differential operators, in complex analysis
    • D. JERISON AND A. SANCHEZ-CALLE, Subelliptic second order differential operators, in Complex Analysis, Lecture Notes in Math. 1277 (1988).
    • (1988) Lecture Notes in Math. , vol.1277
    • Jerison, D.1    Sanchez-Calle, A.2
  • 22
    • 0001207007 scopus 로고
    • Weighted Poincaré and Sobolev inequalities for vector fields satisfying Hörmander's condition and applications
    • G. LU, Weighted Poincaré and Sobolev inequalities for vector fields satisfying Hörmander's condition and applications, Revista Mat. Iberoamericana 8 (1992), 367-439.
    • (1992) Revista Mat. Iberoamericana , vol.8 , pp. 367-439
    • Lu, G.1
  • 23
    • 0000157670 scopus 로고
    • The sharp Poincaré inequality for free vector fields: An endpoint result
    • _, The sharp Poincaré inequality for free vector fields: An endpoint result, Revista Mat. Iberoamericana 10 (1994), 453-466.
    • (1994) Revista Mat. Iberoamericana , vol.10 , pp. 453-466
  • 24
    • 21844500588 scopus 로고
    • Analyse sur les boules d'un opérateur souselliptiques
    • P. MAHEUX AND L. SALOFF-COSTE, Analyse sur les boules d'un opérateur souselliptiques. Math. Ann. 303 (1995), 713-740.
    • (1995) Math. Ann. , vol.303 , pp. 713-740
    • Maheux, P.1    Saloff-Coste, L.2
  • 25
    • 0041862120 scopus 로고
    • Balls and metrics defined by vector fields I: Basic properties
    • A. NAGEL, E. M. STEIN AND S. WAINGER, Balls and metrics defined by vector fields I: basic properties, Acta Math. 155 (1985), 103-147.
    • (1985) Acta Math. , vol.155 , pp. 103-147
    • Nagel, A.1    Stein, E.M.2    Wainger, S.3
  • 26
    • 0000691746 scopus 로고
    • Fundamental solutions and geometry of the sums of squares of vector fields
    • A. SANCHEZ-CALLE, Fundamental solutions and geometry of the sums of squares of vector fields, Invent. Math. 78 (1984), 143-160.
    • (1984) Invent. Math. , vol.78 , pp. 143-160
    • Sanchez-Calle, A.1
  • 27
    • 0000444043 scopus 로고
    • Weighted inequalities jor fractional integrals on Euclidean and homogeneous spaces
    • E. T. SAWYER AND R. L. WHEEDEN, Weighted inequalities jor fractional integrals on Euclidean and homogeneous spaces, Amer. J. Math. 114 (1992), 813-874.
    • (1992) Amer. J. Math. , vol.114 , pp. 813-874
    • Sawyer, E.T.1    Wheeden, R.L.2
  • 28
    • 84966241128 scopus 로고
    • Poincaré and Sobolev inequalities in product spaces
    • X. SHI AND A. TORCHINSKY, Poincaré and Sobolev inequalities in product spaces, PTOC. Amer. Math. Soc. 118 (1993), 1117-1124.
    • (1993) PTOC. Amer. Math. Soc. , vol.118 , pp. 1117-1124
    • Shi, X.1    Torchinsky, A.2
  • 29
    • 0010000261 scopus 로고
    • A characterization of some weighted norm inequalities for the fractional maximal function
    • R. L. WHEEDEN, A characterization of some weighted norm inequalities for the fractional maximal function, Studia Math. 107 (1993), 257-272.
    • (1993) Studia Math. , vol.107 , pp. 257-272
    • Wheeden, R.L.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.