Some remarks on sets of uniform convergence
Some remarks on spaces of Morrey type.
Some remarks on strong approximation by Cesàro means
Some remarks on strong factorization of tent spaces
We provide new assertions on factorization of tent spaces.
Some remarks on the dyadic Rademacher maximal function
Properties of a maximal function for vector-valued martingales were studied by the author in an earlier paper. Restricting here to the dyadic setting, we prove the equivalence between (weighted) inequalities and weak type estimates, and discuss an extension to the case of locally finite Borel measures on ℝⁿ. In addition, to compensate for the lack of an inequality, we derive a suitable BMO estimate. Different dyadic systems in different dimensions are also considered.
Some remarks on the unified characterization of reproducing systems.
The affine systems generated by Ψ ⊂ L2(Rn) are the systemsAA(Ψ) = {DjA Tk Ψ : j ∈ Z, k ∈ Zn},where Tk are the translations, and DA the dilations with respect to an invertible matrix A. As shown in [5], there is a simple characterization for those affine systems that are a Parseval frame for L2(Rn). In this paper, we correct an error in the proof of the characterization result from [5], by redefining the class of not-necessarily expanding dilation matrices for which this characterization result holds....
Some remarks on variational problems for functionals with growth
Some results about the Henstock-Kurzweil Fourier transform
We consider the Fourier transform in the space of Henstock-Kurzweil integrable functions. We prove that the classical results related to the Riemann-Lebesgue lemma, existence and continuity are true in appropriate subspaces.
Some results in spectral analysis and synthesis at infinity.
Some results in the metric theory of tensor products
Some results on biorthogonal polynomials.
Some results on function spaces of varying smoothness
This paper deals with function spaces of varying smoothness , where the function :x ↦ s(x) determines the smoothness pointwise. Those spaces were defined in [2] and treated also in [3]. Here we prove results about interpolation, trace properties and present a characterization of these spaces based on differences.
Some results on -approximation of the -th derivate of Fourier series.
Some Sawyer type inequalities for martingales
Some martingale analogues of Sawyer's two-weight norm inequality for the Hardy-Littlewood maximal function Mf are shown for the Doob maximal function of martingales.
Some Sharp Restriction Theorems for Homogenous Manifolds.
Some sharp weighted estimates for multilinear operators.
Some singular measures on the circle which improve spaces
Some spherical uniqueness theorems for multiple trigonometric series.
Some translation-invariant Banach function spaces which contain c₀
We produce several situations where some natural subspaces of classical Banach spaces of functions over a compact abelian group contain the space c₀.
Some types of lacunary Fourier series