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Harmonic functions with boundary values on Herz spaces |
Martha GUZMáN-PARTIDA() |
Departamento de Matemáticas, Universidad de Sonora, Rosales y Luis Encinas, Hermosillo, Sonora, 83000, México |
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Abstract We discuss continuity of the Poisson transform on Herz spaces Bp as well as its action on weighted versions of these sets. We also consider Banachvalued versions of Herz spaces and study some of their properties.
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Keywords
Herz space
Poisson transform
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Corresponding Author(s):
GUZMáN-PARTIDA Martha,Email:martha@gauss.mat.uson.mx
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Issue Date: 01 December 2013
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1 |
Alvarez J, Guzmán-Partida M, SkórnikU. ?' -convolvability with the Poisson kernel in the Euclidean case and the product domain case. Studia Math(2) , 2003, 156: 143-163
|
2 |
Beurling A. Construction and analysis of some convolution algebras. Ann Inst Fourier (Grenoble) , 1964, 14: 1-32 doi: 10.5802/aif.172
|
3 |
Chen Y Z, Lau K S. Some new classes of Hardy spaces. J Funct Anal , 1989, 84: 255-278 doi: 10.1016/0022-1236(89)90097-9
|
4 |
Diestel J, Uhl J J. Vector Measures. Mathematical Surveys , Vol 15. Providence: Amer Math Soc, 1977 doi: 10.1090/surv/015
|
5 |
Dinculeanu N. Vector Measures. International Series of Monographs in Pure and Applied Mathematics, Vol 95. Oxford: Pergamon Press, 1967
|
6 |
Feichtinger H. An elementary approach to Wiener’s third Tauberian theorem on the Euclidean n-space. In: Proceedings, Conference at Cortona 1984, Symposia Mathematica 29 . New York: Academic Press, 1987, 267-301
|
7 |
García-Cuerva J. Hardy spaces and Beurling algebras. J Lond Math Soc (2) , 1989, 39: 499-513
|
8 |
García-Cuerva J, Rubio de Francia J L. Weighted Norm Inequalities and Related Topics. Amsterdam: North-Holland, 1985
|
9 |
Guzmán-Partida M. A note on boundary values for the Poisson transform. Mat Vesnik , 2007, 59: 197-204
|
10 |
Herz C. Lipschitz spaces and Bernstein’s theorem on absolutely convergent Fourier transforms. J Appl Math Mech , 1968, 18: 283-324
|
11 |
Hernández, Weiss G, Yang D. The φ-transform and wavelet characterizations of Herztype spaces, Collect Math , 1996, 47: 285-320
|
12 |
Li X, Yang D. Boundedness of some sublinear operators on Herz spaces. Illinois J Math , 1996, 40: 484-501
|
13 |
Lu S, Yang D. The local versions of Hp(?n) spaces at the origin. Studia Math (2) , 1995, 116: 103-131
|
14 |
Lu S, Yang D, Hu G. Herz Type Spaces and Their Applications. Beijing: Science Press, 2008
|
15 |
Matsuoka K. On some weighted Herz spaces and the Hardy-Littlewood maximal operator. Proc Int Symp Banach and Function Spaces II, Kitakyushu, Japan . 2006, 375-384
|
16 |
Wiener N. Generalized harmonic analysis. Acta Math , 1930, 55: 117-258 doi: 10.1007/BF02546511
|
17 |
Wiener N. Tauberian theorems. Ann Math (2) , 1932, 33: 1-100
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