Weighted inequalities of Hardy type
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.
weighted Hardy inequalities for integration operators
maximal Hardy-Littlewood operator in weighted spaces
scientific article; zbMATH DE number 4205085