메뉴 건너뛰기




Volumn 157, Issue 1, 2003, Pages 83-96

Relative Fatou theorem for harmonic functions of rotation invariant stable processes in smooth domains

Author keywords

Relative Fatou theorem; Symmetric stable process; harmonic function

Indexed keywords


EID: 0037782012     PISSN: 00393223     EISSN: None     Source Type: Journal    
DOI: 10.4064/sm157-1-7     Document Type: Article
Times cited : (19)

References (37)
  • 1
    • 0001577515 scopus 로고
    • Principe de Harnack à la frontière et théorème de Fatou pour un opérateur elliptique dans un domaine lipschitzien
    • [A]
    • [A] A. Ancona, Principe de Harnack à la frontière et théorème de Fatou pour un opérateur elliptique dans un domaine lipschitzien, Ann. Inst. Fourier (Grenoble) 28 (1978), no. 4, 169-213.
    • (1978) Ann. Inst. Fourier (Grenoble) , vol.28 , Issue.4 , pp. 169-213
    • Ancona, A.1
  • 4
    • 0002149688 scopus 로고
    • A probabilistic proof of the boundary Harnack principle
    • [BaB] San Diego, CA, 1989, Birkhäuser Boston, Boston, MA, 1990
    • [BaB] R. F. Bass and K. Burdzy, A probabilistic proof of the boundary Harnack principle in: Seminar on Stochastic Processes, 1989 (San Diego, CA, 1989), Birkhäuser Boston, Boston, MA, 1990, 1-16.
    • (1989) Seminar on Stochastic Processes , pp. 1-16
    • Bass, R.F.1    Burdzy, K.2
  • 7
    • 0000760840 scopus 로고
    • On the distribution of first hits for the symmetric stable processes
    • [BGR]
    • [BGR] R. M. Blumenthal, R. K. Getoor and D. B. Ray, On the distribution of first hits for the symmetric stable processes, Trans. Amer. Math. Soc. 99 (1961), 540-554.
    • (1961) Trans. Amer. Math. Soc. , vol.99 , pp. 540-554
    • Blumenthal, R.M.1    Getoor, R.K.2    Ray, D.B.3
  • 8
    • 0031444990 scopus 로고    scopus 로고
    • The boundary Harnack principle for the fractional Laplacian
    • [B1]
    • [B1] K. Bogdan, The boundary Harnack principle for the fractional Laplacian, Studia Math. 123 (1997), 43-80.
    • (1997) Studia Math. , vol.123 , pp. 43-80
    • Bogdan, K.1
  • 9
    • 0001166637 scopus 로고    scopus 로고
    • Representation of α-harmonic functions in Lipschitz domains
    • [B2]
    • [B2] _, Representation of α-harmonic functions in Lipschitz domains, Hiroshima Math. J. 29 (1999), 227-243.
    • (1999) Hiroshima Math. J. , vol.29 , pp. 227-243
  • 10
    • 0034652877 scopus 로고    scopus 로고
    • Sharp estimates for the Green function in Lipschitz domains
    • [B3]
    • [B3] _, Sharp estimates for the Green function in Lipschitz domains, J. Math. Anal. Appl. 243 (2000), 326-337.
    • (2000) J. Math. Anal. Appl. , vol.243 , pp. 326-337
  • 12
    • 0000141096 scopus 로고    scopus 로고
    • Probabilistic proof of boundary Harnack principle for α-harmonic functions
    • [BB1]
    • [BB1] K. Bogdan and T. Byczkowski, Probabilistic proof of boundary Harnack principle for α-harmonic functions, Potential Anal. 11 (1999), 135-156.
    • (1999) Potential Anal. , vol.11 , pp. 135-156
    • Bogdan, K.1    Byczkowski, T.2
  • 13
    • 0002020384 scopus 로고    scopus 로고
    • Potential theory for the α-stable Schrödinger operator on bounded Lipschitz domains
    • [BB2]
    • [BB2] _, _, Potential theory for the α-stable Schrödinger operator on bounded Lipschitz domains, Studia Math. 133 (1999), 53-92.
    • (1999) Studia Math. , vol.133 , pp. 53-92
  • 14
    • 0037579510 scopus 로고    scopus 로고
    • On the Schrödinger operator based on the fractional Laplacian
    • [BB3]
    • [BB3] _, _, On the Schrödinger operator based on the fractional Laplacian, Bull. Polish Acad. Sci. Math. 49 (2001), 291-301.
    • (2001) Bull. Polish Acad. Sci. Math. , vol.49 , pp. 291-301
  • 15
    • 0036628268 scopus 로고    scopus 로고
    • Gradient estimates for harmonic and q-harmonic functions of symmetric stable processes
    • [BKN]
    • [BKN] K. Bogdan, T. Kulczycki and A. Nowak, Gradient estimates for harmonic and q-harmonic functions of symmetric stable processes, Illinois J. Math. 46 (2002), 541-556.
    • (2002) Illinois J. Math. , vol.46 , pp. 541-556
    • Bogdan, K.1    Kulczycki, T.2    Nowak, A.3
  • 17
    • 0032335134 scopus 로고    scopus 로고
    • Estimates on Green function and Poisson kernels for symmetric stable process
    • [CS1]
    • [CS1] Z. Q. Chen and R. Song, Estimates on Green function and Poisson kernels for symmetric stable process, Math. Ann. 312 (1998), 465-501.
    • (1998) Math. Ann. , vol.312 , pp. 465-501
    • Chen, Z.Q.1    Song, R.2
  • 19
    • 0001600528 scopus 로고    scopus 로고
    • Martin boundary and integral representation for harmonic functions of symmetric stable processes
    • [CS3]
    • [CS3] _, _, Martin boundary and integral representation for harmonic functions of symmetric stable processes, J. Funct. Anal. 159 (1998), 267-294.
    • (1998) J. Funct. Anal. , vol.159 , pp. 267-294
  • 21
    • 0017727486 scopus 로고
    • Estimates of harmonic measure
    • [Da]
    • [Da] B. Dahlberg, Estimates of harmonic measure, Arch. Rational Mech. Anal. 65 (1977), 275-288.
    • (1977) Arch. Rational Mech. Anal. , vol.65 , pp. 275-288
    • Dahlberg, B.1
  • 22
    • 0038255067 scopus 로고
    • A relativized Fatou theorem
    • [D1]
    • [D1] J. L. Doob, A relativized Fatou theorem, Proc. Nat. Acad. Sci. U.S.A. 45 (1959), 215-222.
    • (1959) Proc. Nat. Acad. Sci. U.S.A. , vol.45 , pp. 215-222
    • Doob, J.L.1
  • 24
    • 0001737037 scopus 로고
    • Séries trigonométriques et séries de Taylor
    • [F]
    • [F] P. Fatou, Séries trigonométriques et séries de Taylor, Acta Math. 30 (1906), 335-400.
    • (1906) Acta Math. , vol.30 , pp. 335-400
    • Fatou, P.1
  • 26
    • 0002814972 scopus 로고
    • Boundary value problems on Lipschitz domains
    • [JK] W. Littman (ed.), MAA Stud. Math. 23, Math. Assoc. Amer.
    • [JK] D. S. Jerison and C. E. Kenig, Boundary value problems on Lipschitz domains, in: Studies in Partial Differential Equations, W. Littman (ed.), MAA Stud. Math. 23, Math. Assoc. Amer., 1982, 1-68.
    • (1982) Studies in Partial Differential Equations , pp. 1-68
    • Jerison, D.S.1    Kenig, C.E.2
  • 27
    • 0038255066 scopus 로고    scopus 로고
    • Properties of Green function of symmetric stable processes
    • [K]
    • [K] T. Kulczycki, Properties of Green function of symmetric stable processes, Probab. Math. Statist. 17 (1997), 381-406.
    • (1997) Probab. Math. Statist. , vol.17 , pp. 381-406
    • Kulczycki, T.1
  • 30
    • 0038255065 scopus 로고    scopus 로고
    • Martin representation for α-harmonic functions
    • [MS]
    • [MS] K. Michalik and K. Samotij, Martin representation for α-harmonic functions, Probab. Math. Statist. 20 (2000), 75-91.
    • (2000) Probab. Math. Statist. , vol.20 , pp. 75-91
    • Michalik, K.1    Samotij, K.2
  • 31
    • 0037917506 scopus 로고
    • First passage distributions of processes with independent increments
    • [Mi]
    • [Mi] P. W. Millar, First passage distributions of processes with independent increments, Ann. Probab. 3 (1975), 215-233.
    • (1975) Ann. Probab. , vol.3 , pp. 215-233
    • Millar, P.W.1
  • 32
    • 0011444297 scopus 로고
    • Intégrales de Riemann Liouville et potentiels
    • [R1]
    • [R1] M. Riesz, Intégrales de Riemann Liouville et potentiels, Acta Sci. Math. (Szeged) 9 (1938), 1-42.
    • (1938) Acta Sci. Math. (Szeged) , vol.9 , pp. 1-42
    • Riesz, M.1
  • 35
    • 0037917507 scopus 로고    scopus 로고
    • On harmonic measure for Levy processes
    • [Sz]
    • [Sz] P. Sztonyk, On harmonic measure for Levy processes, Probab. Math. Statist. 20 (2000), 383-390.
    • (2000) Probab. Math. Statist. , vol.20 , pp. 383-390
    • Sztonyk, P.1
  • 36
    • 0001356097 scopus 로고
    • Comparisons of kernel functions, boundary Harnack principle and relative Fatou theorem on Lipschitz domains
    • [Wu1]
    • [Wu1] J.-M. Wu, Comparisons of kernel functions, boundary Harnack principle and relative Fatou theorem on Lipschitz domains, Ann. Inst. Fourier (Grenoble) 28 (1978), no. 4, 147-167.
    • (1978) Ann. Inst. Fourier (Grenoble) , vol.28 , Issue.4 , pp. 147-167
    • Wu, J.-M.1
  • 37
    • 0037917508 scopus 로고    scopus 로고
    • Harmonic measures for symmetric stable processes
    • [Wu2]
    • [Wu2] _, Harmonic measures for symmetric stable processes, Studia Math. 149 (2002), 281-293.
    • (2002) Studia Math. , vol.149 , pp. 281-293


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.