Some characterizations of harmonic Bloch and Besov spaces

Xi Fu; Bowen Lu

Czechoslovak Mathematical Journal (2016)

  • Volume: 66, Issue: 2, page 417-430
  • ISSN: 0011-4642

Abstract

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The relationship between weighted Lipschitz functions and analytic Bloch spaces has attracted much attention. In this paper, we define harmonic ω - α -Bloch space and characterize it in terms of ω ( ( 1 - | x | 2 ) β ( 1 - | y | 2 ) α - β ) | f ( x ) - f ( y ) x - y | and ω ( ( 1 - | x | 2 ) β ( 1 - | y | 2 ) α - β ) | f ( x ) - f ( y ) | x | y - x ' | where ω is a majorant. Similar results are extended to harmonic little ω - α -Bloch and Besov spaces. Our results are generalizations of the corresponding ones in G. Ren, U. Kähler (2005).

How to cite

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Fu, Xi, and Lu, Bowen. "Some characterizations of harmonic Bloch and Besov spaces." Czechoslovak Mathematical Journal 66.2 (2016): 417-430. <http://eudml.org/doc/280106>.

@article{Fu2016,
abstract = {The relationship between weighted Lipschitz functions and analytic Bloch spaces has attracted much attention. In this paper, we define harmonic $\omega $-$\alpha $-Bloch space and characterize it in terms of \[ \omega ((1-|x|^2)^\beta (1-|y|^2)^\{\alpha - \beta \}) \Big | \frac\{f(x)-f(y)\}\{x-y\}\Big | \] and \[ \omega ((1-|x|^2)^\beta (1-|y|^2)^\{\alpha - \beta \}) \Big | \frac\{f(x)-f(y)\}\{|x|y-x^\{\prime \}\}\Big | \] where $\omega $ is a majorant. Similar results are extended to harmonic little $\omega $-$\alpha $-Bloch and Besov spaces. Our results are generalizations of the corresponding ones in G. Ren, U. Kähler (2005).},
author = {Fu, Xi, Lu, Bowen},
journal = {Czechoslovak Mathematical Journal},
keywords = {harmonic function; Bloch space; Besov space; majorant},
language = {eng},
number = {2},
pages = {417-430},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Some characterizations of harmonic Bloch and Besov spaces},
url = {http://eudml.org/doc/280106},
volume = {66},
year = {2016},
}

TY - JOUR
AU - Fu, Xi
AU - Lu, Bowen
TI - Some characterizations of harmonic Bloch and Besov spaces
JO - Czechoslovak Mathematical Journal
PY - 2016
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 66
IS - 2
SP - 417
EP - 430
AB - The relationship between weighted Lipschitz functions and analytic Bloch spaces has attracted much attention. In this paper, we define harmonic $\omega $-$\alpha $-Bloch space and characterize it in terms of \[ \omega ((1-|x|^2)^\beta (1-|y|^2)^{\alpha - \beta }) \Big | \frac{f(x)-f(y)}{x-y}\Big | \] and \[ \omega ((1-|x|^2)^\beta (1-|y|^2)^{\alpha - \beta }) \Big | \frac{f(x)-f(y)}{|x|y-x^{\prime }}\Big | \] where $\omega $ is a majorant. Similar results are extended to harmonic little $\omega $-$\alpha $-Bloch and Besov spaces. Our results are generalizations of the corresponding ones in G. Ren, U. Kähler (2005).
LA - eng
KW - harmonic function; Bloch space; Besov space; majorant
UR - http://eudml.org/doc/280106
ER -

References

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