## Abstract Fu and Lu et al. 7 showed that the commutator \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathcal {H}\_{\beta ,b}$\end{document} generated by the fractional Hardy operator and a locally integrable function __b__ is bounded on the homogenous Herz spaces
Commutators of generalized Hardy operators
β Scribed by Zunwei Fu; Shanzhen Lu
- Publisher
- John Wiley and Sons
- Year
- 2009
- Tongue
- English
- Weight
- 149 KB
- Volume
- 282
- Category
- Article
- ISSN
- 0025-584X
No coin nor oath required. For personal study only.
β¦ Synopsis
Abstract
Let__H~a,b~__ be the commutator generated by the generalized Hardy operator and the CMO function. The (L^p^, L^p^) boundedness of H~a,b~ is discussed in this paper. Furthermore, the authors consider the boundedness of H~a,b~ on the weighted homogeneous Herz spaces (Β© 2009 WILEYβVCH Verlag GmbH & Co. KGaA, Weinheim)
π SIMILAR VOLUMES
We show that if 0p -Ο± then the operator Gf s H f z dr 1 y z β«Ε½ . p p Ε½ < <. maps the Hardy space H to L d if and only if is a Carleson measure. Ε½ . Here β« is the usual nontangential approach region with vertex on the unit and d is arclength measure on the circle. We also show that if 0p F 1, β€ ) 0
## Abstract Let __L__ be the infinitesimal generator of an analytic semigroup on __L__^2^(β^__n__^ ) with Gaussian kernel bound, and let __L__^β__Ξ±__ /2^ be the fractional integral of __L__ for 0 < __Ξ±__ < __n__. Suppose that __b__ = (__b__~1~, __b__~2~, β¦, __b__~__m__~ ) is a finite family of loca
## Dedicated to A. Uhhnann i n h o r a o e c r of his eixtkth birthday and a. La8m.e~ in hollour of hi8 fiftieth birthday By E. SOHOLZ and W. TIMMEBMANN of Dresden