An embedding theorem for a weighted space of Sobolev type and correct solvability of the Sturm-Liouville equation
An embedding theorem for Campanato spaces.
An embedding theorem for Sobolev type functions with gradients in a Lorentz space
The purpose of this paper is to prove an embedding theorem for Sobolev type functions whose gradients are in a Lorentz space, in the framework of abstract metric-measure spaces. We then apply this theorem to prove absolute continuity and differentiability of such functions.
An essay on the Interpolation Theorem of Józef Marcinkiewicz - Polish patriot
An estimate in the spirit of Poincaré's inequality
An estimate of the essential norm of a composition operator from to in the unit ball.
An estimation of the Lebesgue functions of biorthogonal systems with an application to the non-existence of some bases in C and
An evaluating characterization of homomorphisms
This work provides an evaluating complete description of positive homomorphisms on an arbitrary algebra of real-valued functions.
An example of a continuum of pairwise non-isomorphic spaces of -functions
An example of a reflexive Lorentz Gamma space with trivial Boyd and Zippin indices
We show that for every there exists a weight such that the Lorentz Gamma space is reflexive, its lower Boyd and Zippin indices are equal to zero and its upper Boyd and Zippin indices are equal to one. As a consequence, the Hardy-Littlewood maximal operator is unbounded on the constructed reflexive space and on its associate space .
An example of a Ф-algebra whose uniform closure is a ring of continuous functions
An existence theorem for the Urysohn integral equation in Banach spaces
An extension of Choquet boundary theory to certain partially ordered compact convex sets
An extension of Whitney's spectral theorem
An identity for reproducing kernels in a planar domain and Hilbert-Schmidt Hankel operators.
An ill-posed nonlocal two-point problem for systems of partial differential equations.
An imbedding theorem for H°(G,Ω)-spaces
An indecomposable Banach space of continuous functions which has small density
Using the method of forcing we construct a model for ZFC where CH does not hold and where there exists a connected compact topological space K of weight such that every operator on the Banach space of continuous functions on K is multiplication by a continuous function plus a weakly compact operator. In particular, the Banach space of continuous functions on K is indecomposable.
An inequality for the indefinite integral of a function in
An inequality in Orlicz function spaces with Orlicz norm
We use Simonenko quantitative indices of an -function to estimate two parameters and in Orlicz function spaces with Orlicz norm, and get the following inequality: , where and are Simonenko indices. A similar inequality is obtained in with Orlicz norm.