An abstract uniform boundedness result
An abstract version of Herz' imbedding theorem
An algebraic characterization of complete inner product spaces.
An algebraic view of distributions and operators
An Almost Orthogonal Radial Wavelet Expansion for Radial Distributions.
An analogue of the Riesz-representation theorem.
An answer to a question of Arhangel'skii
We prove that there exists an example of a metrizable non-discrete space , such that but where and is the space of all continuous functions from into reals equipped with the topology of pointwise convergence. It answers a question of Arhangel’skii ([2, Problem 4]).
An application of a theorem of Hirsberg and Lazar.
An application of averaging operators to multilinearity.
An application of interpolation theory to Fourier series
An application of the generalized Maligranda–Orlicz's Lemma.
An application of the theory of edge Sobolev spaces to weakly hyperbolic operators
An approximation theorem in higher order Orlicz-Sobolev spaces and applications
An atomic decomposition of the predual of BMO(ρ).
We study the Orlicz type spaces Hω, defined as a generalization of the Hardy spaces Hp for p ≤ 1. We obtain an atomic decomposition of Hω, which is used to provide another proof of the known fact that BMO(ρ) is the dual space of Hω (see S. Janson, 1980, [J]).
An elementary approach to some questions in higher order smoothness in Banach spaces.
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.