Harmonic functions with boundary values on Herz spaces

Martha Guzmán-Partida

Front. Math. China ›› 2013, Vol. 8 ›› Issue (6) : 1265-1274.

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Front. Math. China ›› 2013, Vol. 8 ›› Issue (6) : 1265-1274. DOI: 10.1007/s11464-013-0324-8
Research Article
RESEARCH ARTICLE

Harmonic functions with boundary values on Herz spaces

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Abstract

We discuss continuity of the Poisson transform on Herz spaces B p 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.

Keywords

Herz space / Poisson transform

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Martha Guzmán-Partida. Harmonic functions with boundary values on Herz spaces. Front. Math. China, 2013, 8(6): 1265‒1274 https://doi.org/10.1007/s11464-013-0324-8

References

[1.]
Alvarez J, Guzmán-Partida M, Skórnik U. S′-convolvability with the Poisson kernel in the Euclidean case and the product domain case. Studia Math (2), 2003, 156: 143-163
CrossRef Google scholar
[2.]
Beurling A. Construction and analysis of some convolution algebras. Ann Inst Fourier (Grenoble), 1964, 14: 1-32
CrossRef Google scholar
[3.]
Chen Y Z, Lau K S. Some new classes of Hardy spaces. J Funct Anal, 1989, 84: 255-278
CrossRef Google scholar
[4.]
Diestel J, Uhl J J. Vector Measures, 1977, Providence: Amer Math Soc
CrossRef Google scholar
[5.]
Dinculeanu N. Vector Measures, 1967, Oxford: Pergamon Press
[6.]
Feichtinger H. An elementary approach to Wiener’s third Tauberian theorem on the Euclidean n-space. Proceedings, Conference at Cortona 1984, Symposia Mathematica 29, 1987, New York: Academic Press 267 301
[7.]
García-Cuerva J. Hardy spaces and Beurling algebras. J Lond Math Soc (2), 1989, 39: 499-513
CrossRef Google scholar
[8.]
García-Cuerva J, Rubio de Francia J L. Weighted Norm Inequalities and Related Topics, 1985, Amsterdam: North-Holland
[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(ℝn) spaces at the origin. Studia Math (2), 1995, 116: 103-131
[14.]
Lu S, Yang D, Hu G. Herz Type Spaces and Their Applications, 2008, Beijing: Science Press
[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
CrossRef Google scholar
[17.]
Wiener N. Tauberian theorems. Ann Math (2), 1932, 33: 1-100
CrossRef Google scholar
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