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WEIGHTED HOLOMORPHIC BESOV SPACES AND THEIR BOUNDARY VALUES

WEIGHTED HOLOMORPHIC BESOV SPACES AND THEIR BOUNDARY VALUES
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摘要 We study weighted holomorphic Besov spaces and their boundary values. Under certain restrictions on the weighted function and parameters, we establish the equivalent norms for holomorphic functions in terms of their boundary functions. Some results about embedding and interpolation are also included. We study weighted holomorphic Besov spaces and their boundary values. Under certain restrictions on the weighted function and parameters, we establish the equivalent norms for holomorphic functions in terms of their boundary functions. Some results about embedding and interpolation are also included.
作者 V.S.Guliyev
机构地区 University of Alabama
出处 《Analysis in Theory and Applications》 2005年第2期143-156,共14页 分析理论与应用（英文刊）
基金 Both authors are supported in part by the Azerbaijan-U.S. Bilateral Grants Program (project ANSF Award / 3102)The second author is also supported in part by NSF grant, DMS 0200587
关键词 holomorphic Besov space weighted Lebesgue space Poisson kernel singular integral weighted Besov space holomorphic Besov space, weighted Lebesgue space, Poisson kernel, singular integral, weighted Besov space
分类号 O175.8 [理学—基础数学]
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参考文献9

  • 1Guliev, V. S. and Lizorkin, P. L,B-and C-Spaces of Harmonic and Holomorphic Functions, and Classes of Boundary Values. Dokl. Akad. Nauk SSSR, 319(1991), 806-809; English transl, in Soviet Math. Dokl. 44 (1992).
  • 2Schmeisser, H. J. and Hans Triebel, Topics in Fourier Analysis and Function Spaces, Academische Verlag. Geest. Portig, Leipzig, and Wiley, Ctlichester, 1987.
  • 3Muckenhoupt, B., Weighted Norm Inequalities for the Hardy Maximal Functions, Trans. Amer.Math. Soc. 165 (1972), 207-226.
  • 4Besov, O. V., hlvestigations in the Theory of Spaces of Differentiable Functions of Several Variables,Trudy Mat. Inst. Steklov, 182 (1988), 68-127; English transl, in Proc. Steklov Inst. Math. 1(1990),182.
  • 5Kazaxyan, K. S. and Lizorkin, P. I., Multipliers, Bases, and Unconditional Bases in the Weighted Spaces B and SB. Trudy Mat. Inst. Steklov, 187 (1989); English transl, in Proc. Steklov Inst.Math. 3:187(1990), 111-130.
  • 6Kokilashvili, V. and Lizorkin, P. I., Two-Weight Estimates for Multipliers, and Embedding Theorems. Dokl. Akad. Nauk 1994,336 (4), Englisll transl. Russian Acad. Sci. Dokl. Math. 49:3(1994), 515-519.
  • 7Jose L. Rubio de Francia, Vector Valued Inequalities for Fourier Series, Proc. Amer. Math. Soc.,78 (1980), 525-528.
  • 8Jose L.Rubio de Francia, J. L., Ruiz, and Torrea, J.L., Calderon-Zygmund Theory for OperatorValued Kernels, Adv. Math., 62 (1968), 7-48.
  • 9Vyacheslav, S., Rychkov, Littlewood-Paley Theory and Function Spaces with A^locp Weights. Math. Nachr., 224 (2001), 145-180.
Analysis in Theory and Applications
2005年 第2期

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