Displaying similar documents to “On maximal and complete regions”

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...