scholarly journals Weighted Hardy Operators in Complementary Morrey Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Dag Lukkassen ◽  
Lars-Erik Persson ◽  
Stefan Samko
Keyword(s):  
Morrey Spaces ◽  
Bounded Domains ◽  
Weighted Lebesgue Space ◽  
Power Functions ◽  
Logarithmic Factor ◽  
Hardy Type ◽  
Weighted Hardy Operators ◽  
Increasing Function ◽  
Hardy Operators ◽  
Hardy Type Operators

We study the weightedp→q-boundedness of the multidimensional weighted Hardy-type operatorsHwαandℋwαwith radial type weightw=w(|x|), in the generalized complementary Morrey spacesℒ∁{0}p,ψ(ℝn)defined by an almost increasing functionψ=ψ(r). We prove a theorem which provides conditions, in terms of some integral inequalities imposed onψandw, for such a boundedness. These conditions are sufficient in the general case, but we prove that they are also necessary when the functionψand the weightware power functions. We also prove that the spacesℒ∁{0}p,ψ(Ω)over bounded domains Ω are embedded between weighted Lebesgue spaceLpwith the weightψand such a space with the weightψ, perturbed by a logarithmic factor. Both the embeddings are sharp.

Weighted fractional Hardy operators and their commutators on generalized Morrey spaces over quasi-metric measure spaces

2021 ◽  
Vol 24 (6) ◽  
pp. 1643-1669
Author(s):  
Natasha Samko
Keyword(s):  
Upper Bound ◽  
Morrey Space ◽  
Morrey Spaces ◽  
Target Space ◽  
Metric Measure Spaces ◽  
Generalized Morrey Spaces ◽  
Hardy Type ◽  
Measure Spaces ◽  
Hardy Operators ◽  
Hardy Type Operators

Abstract We study commutators of weighted fractional Hardy-type operators within the frameworks of local generalized Morrey spaces over quasi-metric measure spaces for a certain class of “radial” weights. Quasi-metric measure spaces may include, in particular, sets of fractional dimentsions. We prove theorems on the boundedness of commutators with CMO coefficients of these operators. Given a domain Morrey space 𝓛 p,φ (X) for the fractional Hardy operators or their commutators, we pay a special attention to the study of the range of the exponent q of the target space 𝓛 q,ψ (X). In particular, in the case of classical Morrey spaces, we provide the upper bound of this range which is greater than the known Adams exponent.

scholarly journals Weighted Hardy operators in local generalized Orlicz-Morrey spaces

2021 ◽  
Vol 13 (2) ◽  
pp. 522-533
Author(s):  
C. Aykol ◽  
Z.O. Azizova ◽  
J.J. Hasanov
Keyword(s):  
Morrey Space ◽  
Sufficient Conditions ◽  
Morrey Spaces ◽  
Strong Type ◽  
Young Functions ◽  
Weighted Hardy Operators ◽  
Hardy Operators

In this paper, we find sufficient conditions on general Young functions $(\Phi, \Psi)$ and the functions $(\varphi_1,\varphi_2)$ ensuring that the weighted Hardy operators $A_\omega^\alpha$ and ${\mathcal A}_\omega^\alpha$ are of strong type from a local generalized Orlicz-Morrey space $M^{0,\,loc}_{\Phi,\,\varphi_1}(\mathbb R^n)$ into another local generalized Orlicz-Morrey space $M^{0,\,loc}_{\Psi,\,\varphi_2}(\mathbb R^n)$. We also obtain the boundedness of the commutators of $A_\omega^\alpha$ and ${\mathcal A}_\omega^\alpha$ from $M^{0,\,loc}_{\Phi,\,\varphi_1}(\mathbb R^n)$ to $M^{0,\,loc}_{\Psi,\,\varphi_2}(\mathbb R^n)$.

scholarly journals A Weighted Variant of Riemann-Liouville Fractional Integrals onℝn

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Zun Wei Fu ◽  
Shan Zhen Lu ◽  
Wen Yuan
Keyword(s):  
Morrey Spaces ◽  
Fractional Integrals ◽  
Bmo Space ◽  
Necessary Condition ◽  
Weight Functions ◽  
Sharp Estimates ◽  
Bmo Spaces ◽  
Weighted Hardy Operators ◽  
Sufficient And Necessary Condition ◽  
Hardy Operators

We introduce certain type of weighted variant of Riemann-Liouville fractional integral onℝnand obtain its sharp bounds on the central Morrey andλ-central BMO spaces. Moreover, we establish a sufficient and necessary condition of the weight functions so that commutators of weighted Hardy operators (with symbols inλ-central BMO space) are bounded on the central Morrey spaces. These results are further used to prove sharp estimates of some inequalities due to Weyl and Cesàro.

On weighted generalized fractional and Hardy-type operators acting between Morrey-type spaces

2017 ◽  
Vol 20 (6) ◽  
Author(s):  
Evgeniya Burtseva ◽  
Natasha Samko
Keyword(s):  
Morrey Spaces ◽  
Fractional Operators ◽  
Generalized Morrey Spaces ◽  
Hardy Type ◽  
Type Spaces ◽  
Hardy Type Operators

AbstractWe study weighted generalized Hardy and fractional operators acting from generalized Morrey spaces

Hardy Type Operators In Local Vanishing Morrey Spaces On Fractal Sets

2015 ◽  
Vol 18 (5) ◽  
Author(s):  
Dag Lukkassen ◽  
Lars-Erik Persson ◽  
Natasha Samko
Keyword(s):  
Morrey Spaces ◽  
Fractional Dimension ◽  
Explicit Dependence ◽  
Generalized Morrey Spaces ◽  
Weighted Estimates ◽  
Fractal Sets ◽  
Hardy Type ◽  
Hardy Type Operators

AbstractWe obtain two-weighted estimates for the Hardy type operators from local generalized Morrey spaces LThe obtained results show the explicit dependence of the mapping properties of the Hardy type operators on the fractional dimension of the set (X, μ, ϱ). An application to spherical Hardy type operators is also given.

scholarly journals The Approximation Numbers of Hardy-Type Operators on Trees

2001 ◽  
Vol 83 (2) ◽  
pp. 390-418 ◽  
Author(s):  
W. D. Evans ◽  
D. J. Harris ◽  
J. Lang
Keyword(s):  
Approximation Numbers ◽  
Hardy Type ◽  
Hardy Type Operators
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