scholarly journals Commutators of the Fractional Hardy Operator on Weighted Variable Herz-Morrey Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Amjad Hussain ◽  
Muhammad Asim ◽  
Muhammad Aslam ◽  
Fahd Jarad
Keyword(s):  
Adjoint Operator ◽  
Morrey Spaces ◽  
Hardy Operator ◽  
Variable Exponents ◽  
Weighted Variable

In the present paper, our aim is to establish the boundedness of commutators of the fractional Hardy operator and its adjoint operator on weighted Herz-Morrey spaces with variable exponents M K ̇ p , q ⋅ α ⋅ , λ w .

scholarly journals Commutators of the Bilinear Hardy Operator on Herz Type Spaces with Variable Exponents

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Shengrong Wang ◽  
Jingshi Xu
Keyword(s):  
Morrey Spaces ◽  
Hardy Operator ◽  
Variable Exponents ◽  
Herz Spaces ◽  
Bmo Functions ◽  
Type Spaces

In this paper, we obtain the boundedness of bilinear commutators generated by the bilinear Hardy operator and BMO functions on products of Herz spaces and Herz-Morrey spaces with variable exponents.

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.

Riesz potentials and Sobolev embeddings on Morrey spaces of variable exponents

2011 ◽  
Vol 56 (7-9) ◽  
pp. 671-695 ◽  
Author(s):  
Yoshihiro Mizuta ◽  
Eiichi Nakai ◽  
Takao Ohno ◽  
Tetsu Shimomura
Keyword(s):  
Morrey Spaces ◽  
Variable Exponents ◽  
Riesz Potentials ◽  
Sobolev Embeddings

TRIEBEL-LIZORKIN-MORREY SPACES ASSOCIATED WITH NONNEGATIVE SELF-ADJOINT OPERATOR

2021 ◽  
Vol 18 (12) ◽  
pp. 2111
Author(s):  
Trần Trí Dũng ◽  
Nguyễn Ngọc Trọng ◽  
Nguyễn Hoàng Trúc
Keyword(s):  
Adjoint Operator ◽  
Morrey Spaces

              Xét L là một toán tử liên hợp không âm trên  sao cho nhân nhiệt của L thỏa mãn điều kiện bị chặn trên Gaussian. Trong bài báo này, chúng tôi giới thiệu không gian Triebel-Lizorkin-Morrey  liên kết với toán tử , trong đó . Chúng tôi chứng minh rằng các không gian mới này thỏa mãn các đặc trưng quan trọng như đặc trưng liên tục theo các hàm bình phương hoặc đặc trưng phân tích nguyên tử.      

Sobolev’s Inequality for Riesz Potentials of Functions in Musielak–Orlicz–Morrey Spaces Over Non-doubling Metric Measure Spaces

2019 ◽  
Vol 63 (2) ◽  
pp. 287-303
Author(s):  
Takao Ohno ◽  
Tetsu Shimomura
Keyword(s):  
Morrey Spaces ◽  
Variable Exponents ◽  
Metric Measure Spaces ◽  
Riesz Potentials ◽  
Sobolev’S Inequality ◽  
Double Phase ◽  
Measure Spaces

AbstractOur aim in this paper is to establish a generalization of Sobolev’s inequality for Riesz potentials $I_{\unicode[STIX]{x1D6FC}(\,\cdot \,),\unicode[STIX]{x1D70F}}f$ of order $\unicode[STIX]{x1D6FC}(\,\cdot \,)$ with $f\in L^{\unicode[STIX]{x1D6F7},\unicode[STIX]{x1D705},\unicode[STIX]{x1D703}}(X)$ over bounded non-doubling metric measure spaces. As a corollary we obtain Sobolev’s inequality for double phase functionals with variable exponents.

scholarly journals Boundedness of Weighted Hardy Operator and Its Adjoint on Triebel-Lizorkin-Type Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Canqin Tang ◽  
Ruohong Zhou
Keyword(s):  
Weight Function ◽  
Adjoint Operator ◽  
Hardy Operator ◽  
Necessary Condition ◽  
Hausdorff Spaces ◽  
Type Spaces ◽  
Sufficient And Necessary Condition

Letp∈[1,∞],q∈[1,∞),τ∈(0,∞), andα∈(0,1)such thatτ>1/p-1/qandα≤n(1/p-τ), letUψbe the weighted Hardy operator andVψits adjoint operator with respect to the weight functionψ. In this paper, the authors establish a sufficient and necessary condition on weight functionψto ensure the boundedness ofUψandVψon the Triebel-Lizorkin-type spacesḞp,qα,τ(ℝn)and their predual spaces, Triebel-Lizorkin-Hausdorff spaces, which unify and generalize the known results onQ-type spaces.

scholarly journals Weighted Estimates for Commutator of Rough p -Adic Fractional Hardy Operator on Weighted p -Adic Herz–Morrey Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Naqash Sarfraz ◽  
Doaa Filali ◽  
Amjad Hussain ◽  
Fahd Jarad
Keyword(s):  
Morrey Spaces ◽  
Hardy Operator ◽  
Lipschitz Spaces ◽  
Weighted Estimates ◽  
Type Spaces ◽  
Current Article ◽  
Symbol Function

The current article investigates the boundedness criteria for the commutator of rough p -adic fractional Hardy operator on weighted p -adic Lebesgue and Herz-type spaces with the symbol function from weighted p -adic bounded mean oscillations and weighted p -adic Lipschitz spaces.

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