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About 10,000 papers for “Maximal function”
Piotr Hajłasz, Zhuomin Liu · arXiv (Cornell University) · 2013
We introduce a notion of maximal potentials and we prove that they form bounded operators from $L^p$ to the homogeneous Sobolev space $\dot{W}^{1,p}$ for all $n/(n-1)
Cited by 1Open access
Piotr Hajłasz, Zhuomin Liu · Proceedings of the American Mathematical Society · 2014
We introduce a notion of maximal potentials and we prove that they form bounded operators from <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper L Superscript p"> <mml:semantics> <mml:msup> <mml:mi>L</mml:mi> <mml:mi>p</mml:mi> </mml:msup> <mml:annotation encoding="application/x-tex">L^p</mml:annotation> </mml:semantics> </mml:math> </inline-formula> to the homogeneous Sobolev space <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="ModifyingAbove upper W With dot Superscript 1 comma p"> <mml:semantics> <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mover> <mml:mi>W</mml:mi> <mml:mo> ˙ </mml:mo> </mml:mover> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mi>p</mml:mi> </mml:mrow> </mml:msup> <mml:annotation encoding="application/x-tex">\dot {W}^{1,p}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> for all <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="n slash left-parenthesis n minus 1 right-parenthesis greater-than p greater-than n"> <mml:semantics> <mml:mrow> <mml:mi>n</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>/</mml:mo> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>n</mml:mi> <mml:mo> − </mml:mo> <mml:mn>1</mml:mn> <mml:mo stretchy="false">)</mml:mo> <mml:mo>></mml:mo> <mml:mi>p</mml:mi> <mml:mo>></mml:mo> <mml:mi>n</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">n/(n-1)>p>n</mml:annotation> </mml:semantics> </mml:math> </inline-formula> . We apply this result to the problem of boundedness of the spherical maximal operator in Sobolev spaces.
Cited by 9Open access
Ju Young Lee, Sanghyuk Lee, Sewook Oh · arXiv (Cornell University) · 2023
We study the elliptic maximal functions defined by averages over ellipses and rotated ellipses which are multi-parametric variants of the circular maximal function. We prove that those maximal functions are bounded on $L^p$ for some $p\neq \infty$. For this purpose, we obtain some sharp multi-parameter local smoothing estimates.
Cited by 0Open access
Ben Krause · Graduate studies in mathematics · 2023
Cited by 3
Georgios Dosidis · Proceedings of the American Mathematical Society · 2020
In dimensions <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="n greater-than-or-equal-to 2"> <mml:semantics> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo> ≥ </mml:mo> <mml:mn>2</mml:mn> </mml:mrow> <mml:annotation encoding="application/x-tex">n\ge 2</mml:annotation> </mml:semantics> </mml:math> </inline-formula> we obtain <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper L Superscript p 1 Baseline left-parenthesis double-struck upper R Superscript n Baseline right-parenthesis times midline-horizontal-ellipsis times upper L Superscript p Super Subscript m Baseline left-parenthesis double-struck upper R Superscript n Baseline right-parenthesis"> <mml:semantics> <mml:mrow> <mml:msup> <mml:mi>L</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>p</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:mrow> </mml:msup> <mml:mo stretchy="false">(</mml:mo> <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="double-struck">R</mml:mi> </mml:mrow> <mml:mi>n</mml:mi> </mml:msup> <mml:mo stretchy="false">)</mml:mo> <mml:mo> × </mml:mo> <mml:mo> ⋯ </mml:mo> <mml:mo> × </mml:mo> <mml:msup> <mml:mi>L</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>p</mml:mi> <mml:mi>m</mml:mi> </mml:msub> </mml:mrow> </mml:msup> <mml:mo stretchy="false">(</mml:mo> <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="double-struck">R</mml:mi> </mml:mrow> <mml:mi>n</mml:mi> </mml:msup> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">L^{p_1}(\mathbb R^n) \times \dots \times L^{p_m}(\mathbb R^n)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> to <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper L Superscript p Baseline left-parenthesis double-struck upper R Superscript n Baseline right-parenthesis"> <mml:semantics> <mml:mrow> <mml:msup> <mml:mi>L</mml:mi> <mml:mi>p</mml:mi> </mml:msup> <mml:mo stretchy="false">(</mml:mo> <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="double-struck">R</mml:mi> </mml:mrow> <mml:mi>n</mml:mi> </mml:msup> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">L^p(\mathbb R^n)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> boundedness for the multilinear spherical maximal function in the largest possible open set of indices and we provide counterexamples that indicate the optimality of our results. Moreover, we obtain weak type and Lorentz space estimates as well as counterexamples in the endpoint cases.
Cited by 0Open access
Ju Young Lee, Sanghyuk Lee, Sewook Oh · Journal of Functional Analysis · 2024
Cited by 3
Zhuomin Liu · 2012
Abstract. We introduce a notion of maximal potentials and we prove that they form bounded operators from L p to the homogeneous Sobolev space ˙ W 1,p for all n/(n − 1) &lt; p &lt; n. We apply this result to the problem of boundedness of the spherical maximal operator in Sobolev spaces. 1.
Cited by 0
Jean-Pierre Rosay · Contemporary mathematics - American Mathematical Society · 1992
Cited by 4
Juan Arias de Reyna · Lecture notes in mathematics · 2002
Cited by 0
심영선 · Open Access System for Information Sharing (Pohang University of Science and Technology) · 2018
Cited by 0
Ben Krause · Graduate studies in mathematics · 2023
Cited by 0
Wojciech Czaja, Weilin Li, Yiran Li et al. · arXiv (Cornell University) · 2021
Inspired by the Hardy-Littlewood maximal function, we propose a novel pooling strategy which is called maxfun pooling. It is presented both as a viable alternative to some of the most popular pooling functions, such as max pooling and average pooling, and as a way of interpolating between these two algorithms. We demonstrate the features of maxfun pooling with two applications: first in the context of convolutional sparse coding, and then for image classification.
Cited by 0Open access
Loukas Grafakos, Yang Dachun · 2012
Cited by 0
Javier Duoandikoetxea · Graduate studies in mathematics · 2000
Cited by 0
R. Vainio · Annals of the New York Academy of Sciences · 1992
It is proved i‐space compatibility for ordered convergence spaces (every maximal chain inherits its own interval topology) is closed under formation of arbitrary products. Some related results (a Dini theorem) for spaces of continuous functions from arbitrary convergence spaces to lattices endowed with order convergence are obtained.
Cited by 0
Abhishek Ghosh, Kalachand Shuin · arXiv (Cornell University) · 2026
In this article, we characterize the range of $α$ for which the helical maximal function is bounded from $L^p(|x|^α)$ to itself for $3
Cited by 0Open access
Keijiro Yabuta · Archiv der Mathematik · 1990
Cited by 16
Juha Kinnunen, Juha Lehrbäck, Antti V. Vähäkangas · Mathematical surveys and monographs · 2021
Cited by 34
Abhishek Ghosh, Kalachand Shuin · arXiv (Cornell University) · 2026
In this article, we characterize the range of $α$ for which the helical maximal function is bounded from $L^p(|x|^α)$ to itself for $3<p<\infty$. Our result is optimal for $4\leq p<\infty,$ except possibly at end-points.
Cited by 0Open access
Bosio , Niccolò · The International Islamic University Malaysia Repository (The International Islamic University Malaysia) · 2021
This thesis is about Lebesgue’s differentiation theorem, progressively trying \nto generalize its statement.
Cited by 0Open access