We point out that in metric spaces Haver’s property is not equivalent to the property introduced by Addis and Gresham. We prove that they are equal when the space has the Hurewicz property. We prove several results about the preservation of Haver’s property in products. We show that if a separable metric space has the Haver property, and the nth power has the Hurewicz property, then the nth pow...

Here is established the global existence of smooth solutions to a generalized nonlinear equation of Schrödinger type in the usual Sobolev spaces H and certain weighted Sobolev spaces by using Leray-Schauder fixed point theorem and delicate a priori estimates.

Optimal sufficient conditions are found in weighted Lorentz spaces for weight functions which provide the boundedness of the Calderón– Zygmund singular integral operator defined on spaces of homogeneous and nonhomogeneous type. 2000 Mathematics Subject Classification: 42B20, 42B25.

Some weighted Ostrowski type integral inequalities for operators and vector-valued functions in Banach spaces are given. Applications for linear operators in Banach spaces and differential equations are also provided.

Weighted inequalities with power-type weights for operators of harmonic analysis, such as maximal and singular integral operators, commutators integrals in grand variable exponent Lebesgue spaces are derived. The defined on quasi-metric measure doubling condition (spaces homogeneous type). proof the result regarding Hardy–Littlewood operator is based appropriate sharp weighted norm estimates we...

Let u be a holomorphic function and φ a holomorphic self-map of the open unit disk D in the complex plane. We give some new characterizations for the boundedness of the weighted composition operators uCφ from Bloch type spaces to Zygmund type spaces in D in terms of u,φ, their derivatives and the n-th power φ of φ. Moreover, we obtain some similar estimates for their essential norms. From which...