scholarly journals Weighted Lebesgue and central Morrey estimates for -adic multilinear Hausdorff operators and its commutators

2021 ◽  
Vol 73 (7) ◽  
pp. 979-1004
Author(s):  
N. M. Chuong ◽  
D. V. Duong ◽  
K. H. Dung
Keyword(s):  
Morrey Spaces ◽  
Muckenhoupt Weights ◽  
Bmo Space ◽  
Morrey Estimates ◽  
Power Weights ◽  
Hausdorff Operators

UDC 517.9 We establish the sharp boundedness of -adic multilinear Hausdorff operators on the product of Lebesgue and central Morrey spaces associated with both power weights and Muckenhoupt weights. Moreover, the boundedness for the commutators of -adic multilinear Hausdorff operators on the such spaces with symbols in central BMO space is also obtained.

The Dirichlet problem for the uniformly elliptic equation in generalized weighted Morrey spaces

2020 ◽  
Vol 57 (1) ◽  
pp. 68-90 ◽  
Author(s):  
Tahir S. Gadjiev ◽  
Vagif S. Guliyev ◽  
Konul G. Suleymanova
Keyword(s):  
Elliptic Equations ◽  
A Priori Estimates ◽  
A Priori ◽  
Morrey Spaces ◽  
Smooth Bounded Domain ◽  
Weighted Morrey Spaces ◽  
Priori Estimates ◽  
Muckenhoupt Class ◽  
Morrey Estimates ◽  
Dirichlet Boundary Problem

Abstract In this paper, we obtain generalized weighted Sobolev-Morrey estimates with weights from the Muckenhoupt class Ap by establishing boundedness of several important operators in harmonic analysis such as Hardy-Littlewood operators and Calderon-Zygmund singular integral operators in generalized weighted Morrey spaces. As a consequence, a priori estimates for the weak solutions Dirichlet boundary problem uniformly elliptic equations of higher order in generalized weighted Sobolev-Morrey spaces in a smooth bounded domain Ω ⊂ ℝn are obtained.

scholarly journals Weighted Hardy and Potential Operators in Morrey Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Natasha Samko
Keyword(s):  
Riesz Potential ◽  
Sufficient Conditions ◽  
Morrey Spaces ◽  
Potential Operator ◽  
Potential Operators ◽  
Riesz Potential Operator ◽  
Power Weights ◽  
The One ◽  
Necessary And Sufficient ◽  
Hardy Type Operators

We study the weightedp→q-boundedness of Hardy-type operators in Morrey spacesℒp,λ(ℝn) (orℒp,λ(ℝ+1) in the one-dimensional case) for a class of almost monotonic weights. The obtained results are applied to a similar weightedp→q-boundedness of the Riesz potential operator. The conditions on weights, both for the Hardy and potential operators, are necessary and sufficient in the case of power weights. In the case of more general weights, we provide separately necessary and sufficient conditions in terms of Matuszewska-Orlicz indices of weights.

scholarly journals Weighted multilinear Hardy operators and commutators

2015 ◽  
Vol 27 (5) ◽  
Author(s):  
Zun Wei Fu ◽  
Shu Li Gong ◽  
Shan Zhen Lu ◽  
Wen Yuan
Keyword(s):  
Necessary Conditions ◽  
Morrey Spaces ◽  
Bmo Space ◽  
Weight Functions ◽  
Lebesgue Spaces ◽  
Sharp Bounds ◽  
Sharp Estimates ◽  
Sufficient And Necessary Conditions ◽  
Hardy Operators

AbstractIn this paper, we introduce a type of weighted multilinear Hardy operators and obtain their sharp bounds on the product of Lebesgue spaces and central Morrey spaces. In addition, we obtain sufficient and necessary conditions of the weight functions so that the commutators of the weighted multilinear Hardy operators (with symbols in central BMO space) are bounded on the product of central Morrey spaces. These results are further used to prove sharp estimates of some inequalities due to Riemann–Liouville and Weyl.

Estimates for parabolic equations with measure data in generalized Morrey spaces

2019 ◽  
Vol 21 (05) ◽  
pp. 1850044
Author(s):  
Chao Zhang
Keyword(s):  
Parabolic Equations ◽  
Morrey Spaces ◽  
Bounded Mean Oscillation ◽  
Parabolic Problems ◽  
Measure Data ◽  
Spatial Gradient ◽  
Irregular Domain ◽  
Variable Formula ◽  
Mean Oscillation ◽  
Morrey Estimates

In this paper, we prove the optimal generalized Morrey estimates for the spatial gradient of the solutions obtained by limits of approximations (SOLA) for a class of parabolic problems with right-hand side measure in a very general irregular domain. The nonlinearity is assumed to be merely measurable only in the time variable [Formula: see text] and belongs to the small bounded mean oscillation (BMO) class as functions of the spatial variable [Formula: see text].

scholarly journals The Weighted Lp and BMO Estimates for Fractional Hausdorff Operators on the Heisenberg Group

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Guohua Zhang ◽  
Qianqian Li ◽  
Qingyan Wu
Keyword(s):  
Heisenberg Group ◽  
Hardy Spaces ◽  
Power Weights ◽  
Hausdorff Operators ◽  
Operator Norms

In the setting of Heisenberg group, we characterize those functions Φ, for which the fractional Hausdorff operators TΦ,β and Hausdorff operators TΦ, T˜Φ are bounded on Lp spaces with power weights, BMO space, and Hardy spaces, respectively. Meanwhile, the corresponding operator norms of TΦ and T˜Φ are worked out.

scholarly journals Morrey estimates for a class of elliptic equations with drift term

2019 ◽  
Vol 9 (1) ◽  
pp. 1333-1350 ◽  
Author(s):  
G. R. Cirmi ◽  
S. D’Asero ◽  
S. Leonardi
Keyword(s):  
Vector Field ◽  
Boundary Value Problem ◽  
Open Subset ◽  
Elliptic Equations ◽  
Symmetric Matrix ◽  
Morrey Spaces ◽  
Drift Term ◽  
Morrey Estimates ◽  
Bounded Open Subset ◽  
And Function

Abstract We consider the following boundary value problem $$\begin{array}{} \displaystyle \begin{cases} - {\rm div}{[M(x)\nabla u - E(x) u]} =f(x) & \text{in}~~ {\it\Omega} \\ u =0 & \text{on}~~ \partial{\it\Omega}, \end{cases} \end{array}$$ where Ω is a bounded open subset of ℝN, with N > 2, M : Ω → ℝN2 is a symmetric matrix, E(x) and f(x) are respectively a vector field and function both belonging to suitable Morrey spaces and we study the corresponding regularity of u and D u.

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