Displaying similar documents to “On the regularity of bilinear maximal operator”

On weak type inequalities for rare maximal functions in ℝⁿ

A. M. Stokolos (2006)

Colloquium Mathematicae

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The study of one-dimensional rare maximal functions was started in [4,5]. The main result in [5] was obtained with the help of some general procedure. The goal of the present article is to adapt the procedure (we call it "dyadic crystallization") to the multidimensional setting and to demonstrate that rare maximal functions have properties not better than the Strong Maximal Function.

Maximal functions and related weight classes.

Carlo Sbordone, Ingemar Wik (1994)

Publicacions Matemàtiques

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The famous result of Muckenhoupt on the connection between weights w in A-classes and the boundedness of the maximal operator in L(w) is extended to the case p = ∞ by the introduction of the geometrical maximal operator. Estimates of the norm of the maximal operators are given in terms of the A-constants. The equality of two differently defined A-constants is proved. Thereby an answer is given to a question posed by R. Johnson. For non-increasing functions on the positive real line a...

Brézis-Gallouët-Wainger type inequality for Besov-Morrey spaces

Yoshihiro Sawano (2010)

Studia Mathematica

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The aim of the present paper is to obtain an inequality of Brézis-Gallouët-Wainger type for Besov-Morrey spaces. We investigate these spaces in a self-contained manner. Also, we verify that our result is sharp.

Partial Ovoids and Partial Spreads of Classical Finite Polar Spaces

De Beule, J., Metsch, K., Klein, A., Storme, L. (2008)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 05B25, 51E20. We survey the main results on ovoids and spreads, large maximal partial ovoids and large maximal partial spreads, and on small maximal partial ovoids and small maximal partial spreads in classical finite polar spaces. We also discuss the main results on the spectrum problem on maximal partial ovoids and maximal partial spreads in classical finite polar spaces. The research of the fourth author was also supported...

A new framework for generalized Besov-type and Triebel-Lizorkin-type spaces

Yiyu Liang, Dachun Yang, Wen Yuan, Yoshihiro Sawano, Tino Ullrich

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In this paper, the authors propose a new framework under which a theory of generalized Besov-type and Triebel-Lizorkin-type function spaces is developed. Many function spaces appearing in harmonic analysis fall under the scope of this new framework. The boundedness of the Hardy-Littlewood maximal operator or the related vector-valued maximal function on any of these function spaces is not required to construct these generalized scales of smoothness spaces. Instead, a key idea used is...