scholarly journals Weak Hardy-Type Spaces Associated with Ball Quasi-Banach Function Spaces II: Littlewood–Paley Characterizations and Real Interpolation

2019 ◽  
Author(s):  
Songbai Wang ◽  
Dachun Yang ◽  
Wen Yuan ◽  
Yangyang Zhang
Keyword(s):  
Function Spaces ◽  
Real Interpolation ◽  
Banach Function Spaces ◽  
Hardy Type ◽  
Type Spaces

scholarly journals Compactness in quasi-Banach function spaces and applications to compact embeddings of Besov-type spaces

2016 ◽  
Vol 146 (5) ◽  
pp. 905-927 ◽  
Author(s):  
António Caetano ◽  
Amiran Gogatishvili ◽  
Bohumír Opic
Keyword(s):  
Besov Spaces ◽  
Function Spaces ◽  
Lebesgue Spaces ◽  
Banach Function Spaces ◽  
Compact Embeddings ◽  
Type Spaces ◽  
Besov Type Spaces

There are two main aims of the paper. The first is to extend the criterion for the precompactness of sets in Banach function spaces to the setting of quasi-Banach function spaces. The second is to extend the criterion for the precompactness of sets in the Lebesgue spaces Lp(ℝn), 1 ⩽ p < ∞, to the so-called power quasi-Banach function spaces. These criteria are applied to establish compact embeddings of abstract Besov spaces into quasi-Banach function spaces. The results are illustrated on embeddings of Besov spaces , into Lorentz-type spaces.

scholarly journals Some s-numbers of an integral operator of Hardy type in Banach function spaces

2016 ◽  
Vol 207 ◽  
pp. 76-97
Author(s):  
David Edmunds ◽  
Amiran Gogatishvili ◽  
Tengiz Kopaliani ◽  
Nino Samashvili
Keyword(s):  
Integral Operator ◽  
Function Spaces ◽  
Banach Function Spaces ◽  
Hardy Type

scholarly journals The boundedness of commutators of rough p-adic fractional Hardy type operators on Herz-type spaces

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Amjad Hussain ◽  
Naqash Sarfraz ◽  
Ilyas Khan ◽  
Abdelaziz Alsubie ◽  
Nawaf N. Hamadneh
Keyword(s):  
Function Spaces ◽  
Type Operator ◽  
Hardy Type ◽  
Type Spaces ◽  
Hardy Type Operator ◽  
Hardy Type Operators

AbstractIn this paper, we obtain some inequalities about commutators of a rough p-adic fractional Hardy-type operator on Herz-type spaces when the symbol functions belong to two different function spaces.

scholarly journals Гранд-пространства типа Морри

2020 ◽  
pp. 104-118
Author(s):  
S.G. Samko ◽  
S.M. Umarkhadzhiev
Keyword(s):  
Integral Operators ◽  
Finite Measure ◽  
Morrey Spaces ◽  
Function Spaces ◽  
Lebesgue Spaces ◽  
Hardy Type ◽  
Grand Lebesgue Spaces ◽  
Type Spaces

The so called grand spaces nowadays are one of the main objects in the theory of function spaces. Grand Lebesgue spaces were introduced by T. Iwaniec and C. Sbordone in the case of sets $\Omega$ with finite measure $|\Omega|<\infty$, and by the authors in the case $|\Omega|=\infty$. The latter is based on introduction of the notion of grandizer. The idea of "grandization" was also applied in the context of Morrey spaces. In this paper we develop the idea of grandization to more general Morrey spaces $L^{p,q,w}(\mathbb{R}^n)$, known as Morrey type spaces. We introduce grand Morrey type spaces, which include mixed and partial grand versions of such spaces. The mixed grand space is defined by the norm $$ \sup_{\varepsilon,\delta} \varphi(\varepsilon,\delta)\sup_{x\in E} \left(\int\limits_{0}^{\infty}{w(r)^{q-\delta}}b(r)^{\frac{\delta}{q}} \left(\,\int\limits_{|x-y|<r}\big|f(y)\big|^{p-\varepsilon} a(y)^{\frac{\varepsilon}{p}}\,dy\right)^{\frac{q-\delta}{p-\varepsilon}} \frac{dr}{r}\right)^{\frac{1}{q-\varepsilon}} $$ with the use of two grandizers $a$ and $b$. In the case of grand spaces, partial with respect to the exponent $q$, we study the boundedness of some integral operators. The class of these operators contains, in particular, multidimensional versions of Hardy type and Hilbert operators.

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