scholarly journals On 2-microlocal Morrey type Besov and Triebel-Lizorkin spaces with variable exponents

2021 ◽  
Vol 110 (124) ◽  
pp. 103-120
Author(s):  
Chenglong Fang
Keyword(s):  
Maximal Functions ◽  
Variable Exponents ◽  
Molecular Decomposition ◽  
Local Means

We introduce 2-microlocal Morrey type Besov and Triebel-Lizorkin spaces with variable exponents and give some characterizations of these spaces by so-called Peetre?s maximal functions. The atomic and molecular decompositions of these spaces are obtained. Finally, using molecular decomposition and the property of local means, we get the wavelet characterizations of these spaces.

scholarly journals Non-smooth atomic decomposition of variable 2-microlocal Besov-type and Triebel–Lizorkin-type spaces

2021 ◽  
Vol 15 (3) ◽  
Author(s):  
Helena F. Gonçalves
Keyword(s):  
Atomic Decomposition ◽  
Morrey Spaces ◽  
Maximal Functions ◽  
Variable Exponents ◽  
Atomic Decompositions ◽  
Local Means ◽  
Essential Tool ◽  
Pointwise Multipliers ◽  
Type Spaces

AbstractIn this paper we provide non-smooth atomic decompositions of 2-microlocal Besov-type and Triebel–Lizorkin-type spaces with variable exponents $$B^{\varvec{w}, \phi }_{p(\cdot ),q(\cdot )}({\mathbb {R}}^n)$$ B p ( · ) , q ( · ) w , ϕ ( R n ) and $$F^{\varvec{w}, \phi }_{p(\cdot ),q(\cdot )}({\mathbb {R}}^n)$$ F p ( · ) , q ( · ) w , ϕ ( R n ) . Of big importance in general, and an essential tool here, are the characterizations of the spaces via maximal functions and local means, that we also present. These spaces were recently introduced by Wu et al. and cover not only variable 2-microlocal Besov and Triebel–Lizorkin spaces $$B^{\varvec{w}}_{p(\cdot ),q(\cdot )}({\mathbb {R}}^n)$$ B p ( · ) , q ( · ) w ( R n ) and $$F^{\varvec{w}}_{p(\cdot ),q(\cdot )}({\mathbb {R}}^n)$$ F p ( · ) , q ( · ) w ( R n ) , but also the more classical smoothness Morrey spaces $$B^{s, \tau }_{p,q}({\mathbb {R}}^n)$$ B p , q s , τ ( R n ) and $$F^{s,\tau }_{p,q}({\mathbb {R}}^n)$$ F p , q s , τ ( R n ) . Afterwards, we state a pointwise multipliers assertion for this scale.

scholarly journals Molecular Decomposition of Anisotropic Hardy Spaces With Variable Exponents

2020 ◽  
Vol 51 (4) ◽  
pp. 1471-1495
Author(s):  
Wenhua Wang ◽  
Xiong Liu ◽  
Aiting Wang ◽  
Baode Li
Keyword(s):  
Hardy Spaces ◽  
Variable Exponents ◽  
Molecular Decomposition

scholarly journals New Herz Type Besov and Triebel-Lizorkin Spaces with Variable Exponents

2012 ◽  
Vol 2012 ◽  
pp. 1-27 ◽  
Author(s):  
Baohua Dong ◽  
Jingshi Xu
Keyword(s):  
Maximal Operator ◽  
Maximal Functions ◽  
Variable Exponents ◽  
Herz Spaces ◽  
Vector Valued ◽  
Littlewood Maximal Operator

The authors establish the boundedness of vector-valued Hardy-Littlewood maximal operator in Herz spaces with variable exponents. Then new Herz type Besov and Triebel-Lizorkin spaces with variable exponents are introduced. Finally, characterizations of these new spaces by maximal functions are given.

scholarly journals Extrapolation to mixed norm spaces and applications

2021 ◽  
Vol 25 (2) ◽  
pp. 281-296
Author(s):  
Kwok-Pun Ho
Keyword(s):  
Lorentz Spaces ◽  
Maximal Functions ◽  
Mixed Norm ◽  
Variable Exponents ◽  
Lebesgue Spaces ◽  
Mixed Norm Spaces ◽  
Special Cases ◽  
Extrapolation Theory

This paper establishes extrapolation theory to mixed norm spaces. By applying this extrapolation theory, we obtain the mapping properties of the Rubio de Francia Littlewood-Paley functions and the geometrical maximal functions on mixed norm spaces. As special cases of these results, we have the mapping properties on the mixed norm Lebesgue spaces with variable exponents and the mixed norm Lorentz spaces.

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