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Self-Improving Properties of Continuous and Discrete Muckenhoupt Weights: A Unified Approach
Axioms, 2023 In this paper, we develop a new technique on a time scale T to prove that the self-improving properties of the Muckenhoupt weights hold. The results contain the properties of the weights when T=R and when T=N, and also can be extended to cover different ...
Maryam M. Abuelwafa +3 more
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AxiomsThis article contains some relations, which include some embedding and transition properties, between the Muckenhoupt classes Mγ;γ>1 and the Gehring classes Gδ;δ>1 of bi-Sobolev weights on a time scale T.
Samir H. Saker +5 more
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On the extension of Muckenhoupt weights in metric spaces [PDF]
Nonlinear Analysis, 2020 A theorem by Wolff states that weights defined on a measurable subset of R n and satisfying a Muckenhoupt-type condition can be extended into the whole space as Muckenhoupt weights of the same class.
Emma-Karoliina Kurki, Carlos Mudarra
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Theory of discrete Muckenhoupt weights and discrete Rubio de Francia extrapolation theorems
Applicable Analysis and Discrete Mathematics, 2021 In this paper, we will prove a discrete Rubio De Francia extrapolation theorem in the theory of discrete Ap-Muckenhoupt weights for which the discrete Hardy-Littlewood maximal operator is bounded on lpw (Z+).
S. Saker, R. Agarwal
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Local Muckenhoupt class for variable exponents
Journal of Inequalities and Applications, 2021 This work extends the theory of Rychkov, who developed the theory of A p loc $A_{p}^{\mathrm{loc}}$ weights. It also extends the work by Cruz-Uribe SFO, Fiorenza, and Neugebauer. The class A p ( ⋅ ) loc $A_{p(\cdot )}^{\mathrm{loc}}$ is defined.
Toru Nogayama, Yoshihiro Sawano
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Uniform approximation of Muckenhoupt weights on fractals by simple functions
Revista de la Unión Matemática Argentina, 2021 . Given an A p -Muckenhoupt weight on a fractal obtained as the attractor of an iterated function system, we construct a sequence of approximating weights, which are simple functions belonging uniformly to the A p class on the approximating spaces.
M. Carena, M. Toschi
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Sobolev Spaces with Non-Muckenhoupt Weights, Fractional Elliptic Operators, and Applications [PDF]
SIAM Journal on Mathematical Analysis, 2018 We propose a new variational model in weighted Sobolev spaces with non-standard weights and applications to image processing. We show that these weights are, in general, not of Muckenhoupt type and therefore the classical analysis tools may not apply ...
H. Antil, Carlos N. Rautenberg
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Structure of a generalized class of weights satisfy weighted reverse Hölder’s inequality
Journal of Inequalities and Applications, 2023 In this paper, we will prove some fundamental properties of the power mean operator M p g ( t ) = ( 1 ϒ ( t ) ∫ 0 t λ ( s ) g p ( s ) d s ) 1 / p , for t ∈ I ⊆ R + , $$ \mathcal{M}_{p}g(t)= \biggl( \frac{1}{\Upsilon(t)} \int _{0}^{t} \lambda (s)g^{p ...
S. H. Saker +3 more
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Global gradient estimates for Dirichlet problems of elliptic operators with a BMO antisymmetric part
Advances in Nonlinear Analysis, 2022 Let n≥2n\ge 2 and Ω⊂Rn\Omega \subset {{\mathbb{R}}}^{n} be a bounded nontangentially accessible domain. In this article, the authors investigate (weighted) global gradient estimates for Dirichlet boundary value problems of second-order elliptic equations
Yang Sibei, Yang Dachun, Yuan Wen
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The maximal operator in weighted variable spaces Lp(⋅)
Journal of Function Spaces and Applications, 2007 We study the boundedness of the maximal operator in the weighted spaces Lp(⋅)(ρ) over a bounded open set Ω in the Euclidean space ℝn or a Carleson curve Γ in a complex plane.
Vakhtang Kokilashvili +2 more
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