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Best Simultaneous Local Approximation in the Lp Norms
(Taylor & Francis, 2017-06)
We study the behavior of the best simultaneous approximation to two functions from a convex set in Lp spaces, 2<p<∞, on a finite union of intervals when its measure tends to zero. In particular, we give sufficient conditions ...
Multipoint Padé approximants as limits of rational functions of best approximation in the complex domain
(Universidad de Jaén, 2018-10)
In this paper we study the behavior of best Lp-approximations by rational functions to an analytic function on union of disks, when the measure of them tends to zero.
Random series in Lp(X, Σ,μ) using unconditional basic sequences and lp stable sequences: A result on almost sure almost everywhere convergence
(American Mathematical Society, 2007-11)
Here we study the almost sure almost everywhere convergence of random series of the form Σ∞ i=1αifi in the Lebesgue spaces L p(X, Σ,μ), where the ai's are centered random variables, and the fi's constitute an unconditional ...
An extrapolation theorem with applications to weighted estimates for singular integrals
(Academic Press Inc Elsevier Science, 2012-05)
We prove an extrapolation theorem saying that the weighted weak type (1; 1) inequality for A1 weights implies the strong Lp(w) bound in terms of the Lp(w) operator norm of the maximal operator M. The weak Muchkenhoupt-Wheeden ...
Some remarks on non-symmetric polarization
(Academic Press Inc Elsevier Science, 2018-10)
Let P:Cn→C be an m-homogeneous polynomial given by P(x)=∑1≤j1≤…≤jm≤ncj1…jm xj1 …xjm . Defant and Schlüters defined a non-symmetric associated m-form LP:(Cn)m→C by LP(x(1),…,x(m))=∑1≤j1≤…≤jm≤ncj1…jm xj1 (1)…xjm (m). They ...
A heat equation with memory: large-time behavior
(Academic Press Inc Elsevier Science, 2021-06)
We study the large-time behavior in all Lp norms of solutions to a heat equation with a Caputo α-time derivative posed in RN (0 < α < 1). These are known as subdiffusion equations. The initial data are assumed to be ...
Lp-dimension free boundedness for Riesz transforms associated to Hermite functions
(Springer, 2004-04)
Riesz transforms associated to Hermite functions were introduced by S. Thangavelu, who proved that they are bounded operators on L^p(R^d ), 1 < p < ∞ . In this paper we give a different proof that allows us to show that ...
Two-Weight Norm Inequalities for the Local Maximal Function
(Springer, 2017-01)
For a local maximal function defined on a certain family of cubes lying “well inside” of Ω , a proper open subset of Rn, we characterize the couple of weights (u, v) for which it is bounded from Lp(v) on Lq(u).
Parabolic mean values and maximal estimates for gradients of temperatures
(Academic Press Inc Elsevier Science, 2008-10)
We aim to prove inequalities of the form | δk - λ (x, t) ∇k u (x, t) | ≤ C MR+- MD#, λ, k u (x, t) for solutions of frac(∂ u, ∂ t) = Δ u on a domain Ω = D × R+, where δ (x, t) is the parabolic distance of (x, t) to parabolic ...
Strong subdifferentiability and local Bishop–Phelps–Bollobás properties
(Real Acad Ciencias Exactas Fisicas & Naturales, 2020-01-02)
Some local versions of the Bishop–Phelps–Bollobás property for operators have been recently presented in Dantas et al. (J Math Anal Appl 468(1):304–323, 2018). In the present article, we continue studying these properties ...