scholarly journals Smooth Decompositions of Triebel-Lizorkin and Besov Spaces on Product Spaces of Homogeneous Type

2014 ◽  
Vol 2014 ◽  
pp. 1-15
Author(s):  
Fanghui Liao ◽  
Zongguang Liu ◽  
Xiaojin Zhang
Keyword(s):  
Besov Spaces ◽  
Homogeneous Type ◽  
Product Spaces ◽  
Spaces Of Homogeneous Type ◽  
Calderón’S Reproducing Formula

We introduce Triebel-Lizorkin and Besov spaces by Calderón’s reproducing formula on product spaces of homogeneous type. We also obtain smooth atomic and molecular decompositions for these spaces.

Frame Characterizations of Besov and Triebel–Lizorkin Spaces on Spaces of Homogeneous Type and their Applications

2002 ◽  
Vol 9 (3) ◽  
pp. 567-590
Author(s):  
Dachun Yang
Keyword(s):  
Besov Spaces ◽  
Interpolation Method ◽  
Real Interpolation ◽  
Homogeneous Type ◽  
Spaces Of Homogeneous Type ◽  
Entropy Numbers ◽  
Compact Embeddings

Abstract The author first establishes the frame characterizations of Besov and Triebel–Lizorkin spaces on spaces of homogeneous type. As applications, the author then obtains some estimates of entropy numbers for the compact embeddings between Besov spaces or between Triebel–Lizorkin spaces. Moreover, some real interpolation theorems on these spaces are also established by using these frame characterizations and the abstract interpolation method.

scholarly journals BMO from dyadic BMO via expectations on product spaces of homogeneous type

2013 ◽  
Vol 265 (10) ◽  
pp. 2420-2451 ◽  
Author(s):  
Peng Chen ◽  
Ji Li ◽  
Lesley A. Ward
Keyword(s):  
Homogeneous Type ◽  
Product Spaces ◽  
Spaces Of Homogeneous Type

scholarly journals Discrete Paraproduct Operators on Variable Hardy Spaces

2019 ◽  
Vol 63 (2) ◽  
pp. 304-317 ◽  
Author(s):  
Jian Tan
Keyword(s):  
Hardy Space ◽  
Hardy Spaces ◽  
Variable Exponent ◽  
Discrete Version ◽  
Variable Exponents ◽  
Homogeneous Type ◽  
Spaces Of Homogeneous Type ◽  
Hölder Continuous ◽  
Analysis Techniques ◽  
Calderón’S Reproducing Formula

AbstractLet$p(\cdot ):\mathbb{R}^{n}\rightarrow (0,\infty )$be a variable exponent function satisfying the globally log-Hölder continuous condition. In this paper, we obtain the boundedness of paraproduct operators$\unicode[STIX]{x1D70B}_{b}$on variable Hardy spaces$H^{p(\cdot )}(\mathbb{R}^{n})$, where$b\in \text{BMO}(\mathbb{R}^{n})$. As an application, we show that non-convolution type Calderón–Zygmund operators$T$are bounded on$H^{p(\cdot )}(\mathbb{R}^{n})$if and only if$T^{\ast }1=0$, where$\frac{n}{n+\unicode[STIX]{x1D716}}<\text{ess inf}_{x\in \mathbb{R}^{n}}p\leqslant \text{ess sup}_{x\in \mathbb{R}^{n}}p\leqslant 1$and$\unicode[STIX]{x1D716}$is the regular exponent of kernel of$T$. Our approach relies on the discrete version of Calderón’s reproducing formula, discrete Littlewood–Paley–Stein theory, almost orthogonal estimates, and variable exponents analysis techniques. These results still hold for variable Hardy space on spaces of homogeneous type by using our methods.

Sign in / Sign up

Export Citation Format

Share Document