Weighted inequalities of Hardy type
type: Item
instance of: scholarly article
title: Weighted inequalities of Hardy type
zbMATH Open document ID: 0729.42007
DOI: 10.1007/BF01054210
author: Eh. N. Batuev
author: V. D. Stepanov
published in: Siberian Mathematical Journal
publication date: 1989-01-01T00:00:00Z
review text: In Section 1 of this paper we present a new method for obtaining weighted Hardy inequalities for integration operators. The indicated method allows us to simplify and unify the known results of B. Muckenhoupt, V. G. Maz'ya, V. M. Kokilashvili and other authors on integration operators. In Section 2 we obtain weighted estimates for the Steklov operators. A particular case of these estimates is Muckenhoupt's theorem on the boundedness of the maximal Hardy-Littlewood operator in weighted spaces. As an application of the statements regarding the Steklov operators, we give an a priori estimate in weighted norms (necessary and sufficient conditions) of the solutions of the Cauchy problem for the wave equation.
Mathematics Subject Classification ID: 42B25
Mathematics Subject Classification ID: 26D10
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 35B45
zbMATH DE Number: 4205085
zbMATH Keywords: weighted Hardy inequalities for integration operators
zbMATH Keywords: Steklov operators
zbMATH Keywords: Muckenhoupt's theorem
zbMATH Keywords: boundedness
zbMATH Keywords: maximal Hardy-Littlewood operator in weighted spaces
zbMATH Keywords: Cauchy problem
zbMATH Keywords: wave equation
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4205085