Some essential properties ofQ
p
(?Δ)-spaces |
| |
Authors: | Jie Xiao Jie Xiao |
| |
Institution: | (1) Present address: Department of Mathematics, Peking University, 100871 Beijing, China;(2) Present address: Institute of Analysis, TU Braunschweig, PK 14, D-38106, Germany |
| |
Abstract: | For p∈(?∞, ∞) letQ p (?Δ) be the space of all complex-valued functions f on the unit circle ?Δ satisfying $\mathop {\sup }\limits_{I \subset \partial \Delta } \left| I \right|^{ - p} \int_I {\int_I {\frac{{\left| {f(z) - f(w)} \right|^2 }}{{\left| {z - w} \right|^{2 - p} }}\left| {dz} \right|\left| {dw} \right|< \infty } } $ , where the supremum is taken over all subarcs I ? ?Δ with the arclength |I|. In this paper, we consider some essential properties ofQ p (?Δ). We first show that if p>1, thenQ p (?Δ)=BMO(?Δ), the space of complex-valued functions with bounded mean oscillation on ?Δ. Second, we prove that a function belongs toQ p (?Δ) if and only if it is Möbius bounded in the Sobolev spaceL p 2 (?Δ). Finally, a characterization ofQ p (?Δ) is given via wavelets. |
| |
Keywords: | Math Subject Classifications" target="_blank">Math Subject Classifications 42A45 46E15 |
本文献已被 SpringerLink 等数据库收录! |
|