scholarly journals Boundedness of Mikhlin Operator in Variable Exponent Morrey Space

2021 ◽  
Vol 2 (1) ◽  
pp. 79-85
Author(s):  
Morteza Koozehgar Kalleji ◽  
Keyword(s):  
Variable Exponent ◽  
Morrey Space

scholarly journals Weighted Hardy-Type Inequalities in Variable Exponent Morrey-Type Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
Dag Lukkassen ◽  
Lars-Erik Persson ◽  
Stefan Samko ◽  
Peter Wall
Keyword(s):  
Variable Exponent ◽  
Morrey Space ◽  
Variable Order ◽  
Generalized Morrey Space ◽  
Hardy Type Inequalities ◽  
Hardy Type ◽  
Radial Weight ◽  
Type Integral ◽  
Type Spaces ◽  
Hardy Type Operators

We study thep·→q·boundedness of weighted multidimensional Hardy-type operatorsHwα·andℋwα·of variable orderαx, with radial weightwx, from a variable exponent locally generalized Morrey spaceℒp·,φ·ℝn,wto anotherℒq·,ψ·ℝn,w. The exponents are assumed to satisfy the decay condition at the origin and infinity. We construct certain functions, defined byp,α, andφ, the belongness of which to the resulting spaceℒq·,ψ·ℝn,wis sufficient for such a boundedness. Under additional assumptions onφ/w, this condition is also necessary. We also give the boundedness conditions in terms of Zygmund-type integral inequalities for the functionsφandφ/w.

scholarly journals Morrey Meets Herz with Variable Exponent and Applications to Commutators of Homogeneous Fractional Integrals with Rough Kernels

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Hongbin Wang ◽  
Jiajia Wang ◽  
Zunwei Fu
Keyword(s):  
Variable Exponent ◽  
Morrey Space ◽  
Homogeneous Function ◽  
Fractional Integrals ◽  
Herz Space ◽  
Degree Zero ◽  
Rough Kernels ◽  
Bmo Function ◽  
Central Morrey Space ◽  
Homogeneous Fractional Integral Operator

We define the new central Morrey space with variable exponent and investigate its relation to the Morrey-Herz spaces with variable exponent. As applications, we obtain the boundedness of the homogeneous fractional integral operator TΩ,σ and its commutator [b,TΩ,σ] on Morrey-Herz space with variable exponent, where Ω∈Ls(Sn-1) for s≥1 is a homogeneous function of degree zero, 0<σ<n, and b is a BMO function.

scholarly journals Some estimates for the commutators of multilinear maximal function on Morrey-type space

2021 ◽  
Vol 19 (1) ◽  
pp. 515-530
Author(s):  
Xiao Yu ◽  
Pu Zhang ◽  
Hongliang Li
Keyword(s):  
Maximal Function ◽  
Morrey Space ◽  
Morrey Spaces ◽  
Bounded Mean Oscillation ◽  
Generalized Morrey Spaces ◽  
Type Space ◽  
Bmo Function ◽  
Mean Oscillation ◽  
Multilinear Maximal Function ◽  
Equivalent Conditions

Abstract In this paper, we study the equivalent conditions for the boundedness of the commutators generated by the multilinear maximal function and the bounded mean oscillation (BMO) function on Morrey space. Moreover, the endpoint estimate for such operators on generalized Morrey spaces is also given.

scholarly journals Variable Anisotropic Hardy Spaces with Variable Exponents

2021 ◽  
Vol 9 (1) ◽  
pp. 65-89
Author(s):  
Zhenzhen Yang ◽  
Yajuan Yang ◽  
Jiawei Sun ◽  
Baode Li
Keyword(s):  
Hardy Spaces ◽  
Variable Exponent ◽  
Atomic Decomposition ◽  
Integral Operators ◽  
Moment Condition ◽  
Variable Exponents ◽  
Hölder Continuous ◽  
Multi Level ◽  
The Moment ◽  
Variable Anisotropy

Abstract Let p(·) : ℝ n → (0, ∞] be a variable exponent function satisfying the globally log-Hölder continuous and let Θ be a continuous multi-level ellipsoid cover of ℝ n introduced by Dekel et al. [12]. In this article, we introduce highly geometric Hardy spaces Hp (·)(Θ) via the radial grand maximal function and then obtain its atomic decomposition, which generalizes that of Hardy spaces Hp (Θ) on ℝ n with pointwise variable anisotropy of Dekel et al. [16] and variable anisotropic Hardy spaces of Liu et al. [24]. As an application, we establish the boundedness of variable anisotropic singular integral operators from Hp (·)(Θ) to Lp (·)(ℝ n ) in general and from Hp (·)(Θ) to itself under the moment condition, which generalizes the previous work of Bownik et al. [6] on Hp (Θ).

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