An elementary construction on nonlinear coherent states associated to generalized Bargmann spaces.
An elementary proof of Komlós-Révész theorem in Hilbert spaces.
An elementary proof of Marcellini Sbordone semicontinuity theorem
The weak lower semicontinuity of the functional is a classical topic that was studied thoroughly. It was shown that if the function is continuous and convex in the last variable, the functional is sequentially weakly lower semicontinuous on . However, the known proofs use advanced instruments of real and functional analysis. Our aim here is to present a proof understandable even for students familiar only with the elementary measure theory.
An elliptic semilinear equation with source term involving boundary measures: the subcritical case.
We study the boundary behaviour of the nonnegative solutions of the semilinear elliptic equation in a bounded regular domain Ω of RN (N ≥ 2),⎧ Δu + uq = 0, in Ω⎨⎩ u = μ, on ∂Ωwhere 1 < q < (N + 1)/(N - 1) and μ is a Radon measure on ∂Ω. We give a priori estimates and existence results. The lie on the study of superharmonic functions in some weighted Marcinkiewicz spaces.
An embedding norm and the Lindqvist trigonometric functions.
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.