Results 11 to 20 of about 75,669 (266)
Weighted inequalities for multilinear fractional integral operators
Collectanea mathematica, 2009 The author considers fractional multilinear integral operators \[ {\mathcal I}_\alpha \vec{f}(x):= \int_{\left({\mathbb R}^n\right)^m } {f_1(y_1) \cdots f_m(y_m)\over \left(|x-y_1|+\dots+|x-y_m|\right)^{nm-\alpha}} d\vec{y}. \] Sufficient conditions for the two weight inequalities \[ \left(\int_{{\mathbb R}^n} (|{\mathcal I}_\alpha\vec{f}|u)^q dx\right)
Kabe Moen
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Fractional integrals, derivatives and integral equations with weighted Takagi–Landsberg functions
Nonlinear Analysis, 2020 In this paper, we find fractional Riemann–Liouville derivatives for the Takagi–Landsberg functions. Moreover, we introduce their generalizations called weighted Takagi–Landsberg functions, which have arbitrary bounded coefficients in the expansion under ...
Vitalii Makogin, Yuliya Mishura
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Sharp weighted bounds for fractional integral operators
Journal of Functional Analysis, 2010 The relationship between the operator norms of fractional integral operators acting on weighted Lebesgue spaces and the constant of the weights is investigated. Sharp boundsare obtained for both the fractional integral operators and the associated fractional maximal functions. As an application improved Sobolev inequalities are obtained.
Lacey, Michael T. +3 more
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On Weighted Fractional Integral Inequalities
Journal of Functional Analysis, 2001 The author studies weighted positivity of a fractional power \((-\Delta)^\lambda\) of the Laplace operator, the weight function being the fundamental solution of this fractional power. Let \[ f(n,\lambda)=\psi\left(\frac{n}{2}\right)-\psi\left(\frac{n}{2}-\lambda\right)- \psi(\lambda) +\psi(1).
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Sharp weighted bounds for fractional integral operators [PDF]
, 2009 The relationship between the operator norms of fractional integral operators acting on weighted Lebesgue spaces and the constant of the weights is investigated.
Lacey, Michael T. +4 more
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Two-weight norm inequalities for the rough fractional integrals [PDF]
International Journal of Mathematics and Mathematical Sciences, 2001 The authors give the weighted (Lp,Lq)-boundedness of the rough fractional integral operator TΩ,α and the fractional maximal operator MΩ,α with two different weight functions.
Yong Ding, Chin-Cheng Lin
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Weighted norm inequalities for fractional integrals [PDF]
Transactions of the American Mathematical Society, 1974 The principal problem considered is the determination of all nonnegative functions, V ( x ) V(x) , such that ‖ T γ f ( x ) V (
Muckenhoupt, Benjamin +1 more
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Two weighted inequalities for B-fractional integrals [PDF]
Journal of Inequalities and Applications, 2016 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Eroglu, Ahmet +2 more
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Borderline Weighted Estimates for Commutators of Fractional Integrals
Analysis in Theory and Applications, 2022 Let $I_{\alpha,\vec{b}}$ be the multilinear commutators of the fractional integrals $I_{\alpha}$ with the symbol $\vec{b}=(b_1, \cdots,b_k )$. We show that the constant of borderline weighted estimates for $I_{\alpha}$ is $\frac{1}{{\varepsilon}}$, and for $I_{\alpha,{\vec{b}}}$ is $\frac{1}{{\varepsilon}^{k+1}}$ with each $b_i$ belongs to the Orlicz
Wang, Zhidan +2 more
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Weighted norm inequalities for singular and fractional integrals [PDF]
Transactions of the American Mathematical Society, 1971 Inequalities of the form ‖ | x | α T
Muckenhoupt, Benjamin +1 more
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