Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 1201.42015
Tang, Canqin; Zhai, Zhichun
Generalized Poincaré embeddings and weighted Hardy operator on spaces. (English)
[J] J. Math. Anal. Appl. 371, No. 2, 665-676 (2010). ISSN 0022-247X

The well-known Poincaré embedding $\dot{W}^{1,n}(\mathbb{R}^n)\subset \text{BMO}(\mathbb{R}^n)$ and the John-Nirenberg inequality in $\text{BMO}(\mathbb{R}^n)$ are useful tools in modern analysis and partial differential equations. The authors establish the generalized Poincaré embeddings and the John-Nirenberg inequality in the $Q$-type spaces $Q^{\alpha, q}_p(\mathbb{R}^n)$ for all $\alpha \in (0,1)$, $p\in(0,\infty]$ and $q\in[1,\infty]$, which generalizes the corresponding classical results on $\text{BMO}(\mathbb{R}^n)$. Moreover, the authors also give sufficient and necessary conditions on the function $\psi$ to ensure that the corresponding weighted Hardy operator $U_\psi$ and its adjoint, the weighted Cesàro average operator $V_\psi$, are bounded on the spaces $Q^{\alpha, q}_p(\mathbb{R}^n)$.
[Yang Dachun (Beijing)]

MSC 2000:: *42B30 Hp-spaces (Fourier analysis)
46E35 Sobolev spaces and generalizations
42B35 Function spaces arising in harmonic analysis

Keywords: Poincaré embedding; John-Nirenberg inequality; weighted Hardy space; $Q$-space

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]