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Related papers: Weighted Weak-type Inequalities For Fractionally S…

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In this paper, we are devoted to studying some sharp bounds for Hardy type operators on mixed radial-angular type function spaces. In addition, we will establish the sharp weak-type estimates for the fractional Hardy operator and its…

Functional Analysis · Mathematics 2024-02-06 Ronghui Liu , Yanqi Yang , Shuangping Tao

Let $(X, d, \mu)$ be a space of homogeneous type and $\Omega$ an open subset of $X$. Given a bounded operator $T: L^p(\Omega) \to L^q(\Omega)$ for some $1 \le p \le q < \infty$, we give a criterion for $T$ to be of weak type $(p_0, a)$ for…

Functional Analysis · Mathematics 2026-05-14 Bernhard H. Haak , El-Maati Ouhabaz

Let $(X,d,\mu)$ is a space of homogeneous type, we establish a new class of fractional-type variable weights $A_{p(\cdot), q(\cdot)}(X)$. Then, we get the new weighted strong-type and weak-type characterizations for fractional maximal…

Classical Analysis and ODEs · Mathematics 2024-08-13 Xi Cen

Let $L$ be a linear operator in $L^2(\mathbb{R}^n)$ which generates a semigroup $e^{-tL}$ whose kernels $p_t(x,y)$ satisfy the Gaussian upper bound. In this paper, we investigate several kinds of weighted norm inequalities for the conical…

Classical Analysis and ODEs · Mathematics 2020-11-24 Mingming Cao , Zengyan Si , Juan Zhang

We prove weighted estimates for rough bilinear singular integral operators with kernel $$K(y_1, y_2) = \frac{\Omega((y_1,y_2)/|(y_1,y_2)|)}{|(y_1, y_2)|^{2d}},$$ where $y_i \in \mathbb{R}^{d}$ and $\Omega \in L^{\infty}(S^{2d-1})$ with…

Classical Analysis and ODEs · Mathematics 2017-06-21 Alexander Barron

We discuss here a weak and strong type estimate for fractional integral operators on Morrey spaces, where the underlying measure $\mu$ does not always satisfy the doubling condition.

Functional Analysis · Mathematics 2013-05-30 I. Sihwaningrum , Y. Sawano

In this paper, we explore the limiting weak-type behaviors of some integral operators including maximal operators, singular and fractional integral operators and maximal truncated singular integrals et al. Some optimal limiting weak-type…

Classical Analysis and ODEs · Mathematics 2017-10-31 Weichao Guo , Jianxun He , Huoxiong Wu

Let $\{e^{-tL^{\alpha}}\}_{t>0}$ be the fractional Schr\"{o}dinger semigroup associated with $L=-\Delta+V$, where $V$ is a non-negatvie potential belonging to the reverse H\"{o}lder class. In this paper, we establish weighted boundedness…

Classical Analysis and ODEs · Mathematics 2025-09-16 Yanhan Chen

Two classes of fractional type variable weights are established in this paper. The first kind of weights ${A_{\vec p( \cdot ),q( \cdot )}}$ are variable multiple weights, which are characterized by the weighted variable boundedness of…

Classical Analysis and ODEs · Mathematics 2025-02-11 Xi Cen , Qianjun He , Zichen Song , Zihan Wang

In this paper, we investigate the boundedness of bilinear Calder\'on-Zygmund operators $T$ from ${L^{p_1}\left(w_1\right)} \times {L^{p_2}\left(w_2\right)}$ to ${L^{p,\infty}\left(v_{\vec{w}}\right)}$ with the stopping time method, where $1…

Classical Analysis and ODEs · Mathematics 2023-12-22 Linfei Zheng

In this paper, we first introduce some new Morrey type spaces containing generalized Morrey space and weighted Morrey space with two weights as special cases. Then we give the weighted strong type and weak type estimates for fractional…

Classical Analysis and ODEs · Mathematics 2016-03-16 Hua Wang

We improve on several mixed weak type inequalities both for the Hardy-Littlewood maximal function and for Calder\'on-Zygmund operators. These type of inequalities were considered by Muckenhoupt and Wheeden and later on by Sawyer estimating…

Classical Analysis and ODEs · Mathematics 2015-08-05 Sheldy Ombrosi , Carlos Perez , Jorgelina Recchi

In this paper, we first introduce some new classes of weighted amalgam spaces. Then we give the weighted strong-type and weak-type estimates for fractional integral operators $I_\gamma$ on these new function spaces. Furthermore, the…

Classical Analysis and ODEs · Mathematics 2017-12-13 Hua Wang

We study mixed weighted weak-type inequalities for families of functions, which can be applied to study classical operators in harmonic analysis. Our main theorem extends the key result from D. Cruz-Uribe, J.M. Martell and C. Perez,…

Classical Analysis and ODEs · Mathematics 2016-07-21 Carlos Perez , Sheldy Ombrosi

We show some simple sufficient conditions for which the multilinear embedding theorem holds for fractional sparse operators. By verifying these conditions, we establish the theorem for power weights. We also provide Morrey-type sufficient…

Functional Analysis · Mathematics 2026-04-21 Naoya Hatano , Ryota Kawasumi , Hiroki Saito , Hitoshi Tanaka

In this manuscript we provide necessary and sufficient conditions for the $\textnormal{weak}(1,p)$ boundedness, $1< p<\infty,$ of discrete Fourier multipliers (Fourier multipliers on $\mathbb{Z}^n$). Our main goal is to apply the results…

Functional Analysis · Mathematics 2019-01-23 Duván Cardona

In this paper, we prove bilinear sparse domination bounds for a wide class of Fourier integral operators of general rank, as well as oscillatory integral operators associated to H\"ormander symbol classes $S^m_{\rho,\delta}$ for all…

Classical Analysis and ODEs · Mathematics 2023-09-15 Tobias Mattsson

In this paper quantitative weighted matrix estimates for vector valued extensions of $L^{r'}$-H\"ormander operators and rough singular integrals are studied. Strong type $(p,p)$ estimates, endpoint estimates, and some new results on…

Classical Analysis and ODEs · Mathematics 2021-03-25 Pamela A. Muller , Israel P. Rivera-Ríos

We establish a weighted inequality for fractional maximal and convolution type operators, between weak Lebesgue spaces and Wiener amalgam type spaces on $ \mathbb R $ endowed with a measure which needs not to be doubling.

Classical Analysis and ODEs · Mathematics 2018-10-05 Aïssata Adama , Justin Feuto , Ibrahim Fofana

We give a quantitative characterization of the pairs of weights $(w,v)$ for which the dyadic version of the one-sided Hardy-Littlewood maximal operator satisfies a restricted weak $(p,p)$ type inequality, for $1\leq p<\infty$. More…

Classical Analysis and ODEs · Mathematics 2021-05-25 Fabio Berra