$${\cal N}\left( {p,q,s} \right)$$-Type Spaces in the Unit Ball of ℂn. IV: Atomic Decomposition, Gleason’s Problem and Distance Problems

2021 ◽  
Vol 47 (1) ◽  
pp. 123-148
Author(s):  
B. Hu ◽  
S. Li
Keyword(s):  
Unit Ball ◽  
Atomic Decomposition ◽  
Type Spaces ◽  
Gleason’S Problem

scholarly journals О новых точных теоремах разложения для многофункциональных пространств типа ВМОА в ограниченных псевдовыпуклых областях

2020 ◽  
pp. 102-113
Author(s):  
R.F. Shamoyan ◽  
E.B. Tomashevskaya
Keyword(s):  
Unit Ball ◽  
Atomic Decomposition ◽  
Pseudoconvex Domains ◽  
Type Space ◽  
Type Spaces ◽  
Equivalent Expressions

We provide new equivalent expressions in the unit ball and pseudoconvex domains for multifunctional analytic BMOA type space. We extend in various directions a known theorem of atomic decomposition of BMOA type spaces in the unit ball. Мы приводим новые эквивалентные выражения в единичных шаровых и псевдовыпуклых областях для многофункционального аналитического пространства типа BMOA. Мы расширяем в различных направлениях известную теорему атомарного разложения пространств типа BMOA в единичном шаре.

The Gleason’s Problem on F(p,q,s) Type Spaces in the Unit Ball of $$\mathbf{C^{n}}$$ C n

2017 ◽  
Vol 12 (5) ◽  
pp. 1251-1265 ◽  
Author(s):  
Xuejun Zhang ◽  
Yuting Guo ◽  
Qingli Shang ◽  
Shenlian Li
Keyword(s):  
Unit Ball ◽  
Type Spaces ◽  
Gleason’S Problem

scholarly journals Hadamard gap series in weighted-type spaces on the unit ball

2017 ◽  
Vol 8 (2) ◽  
pp. 259-269 ◽  
Author(s):  
Bingyang Hu ◽  
Songxiao Li
Keyword(s):  
Unit Ball ◽  
Gap Series ◽  
Type Spaces ◽  
Weighted Type

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 On an Integral-Type Operator from Zygmund-Type Spaces to Mixed-Norm Spaces on the Unit Ball

2010 ◽  
Vol 2010 ◽  
pp. 1-7 ◽  
Author(s):  
Stevo Stević
Keyword(s):  
Unit Ball ◽  
Type Operator ◽  
Mixed Norm ◽  
Integral Type ◽  
Mixed Norm Space ◽  
Mixed Norm Spaces ◽  
Norm Space ◽  
Type Spaces

The boundedness and compactness of an integral-type operator recently introduced by the author from Zygmund-type spaces to the mixed-norm space on the unit ball are characterized here.

scholarly journals Bloch type spaces on the unit ball of a Hilbert space

2018 ◽  
Vol 69 (3) ◽  
pp. 695-711
Author(s):  
Zhenghua Xu
Keyword(s):  
Hilbert Space ◽  
Unit Ball ◽  
Type Spaces
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