Weighted weak type (1,1) estimates for oscillatory singular integrals
We consider the -weights and prove the weighted weak type (1,1) inequalities for certain oscillatory singular integrals.
Weighted weak type (1,1) estimates for singular integrals and Littlewood-Paley functions
We prove some weighted weak type (1,1) inequalities for certain singular integrals and Littlewood-Paley functions.
Weighted weak type inequalities for certain maximal functions
We give an A_p type characterization for the pairs of weights (w,v) for which the maximal operator Mf(y) = sup 1/(b-a) ʃ_a^b |f(x)|dx, where the supremum is taken over all intervals [a,b] such that 0 ≤ a ≤ y ≤ b/ψ(b-a), is of weak type (p,p) with weights (w,v). Here ψ is a nonincreasing function such that ψ(0) = 1 and ψ(∞) = 0.
Weighted weak-type inequalities for generalized Hardy operators.
Weil Multipliers.
Well-posedness of second order degenerate differential equations in vector-valued function spaces
Using known results on operator-valued Fourier multipliers on vector-valued function spaces, we give necessary or sufficient conditions for the well-posedness of the second order degenerate equations (P₂): d/dt (Mu’)(t) = Au(t) + f(t) (0 ≤ t ≤ 2π) with periodic boundary conditions u(0) = u(2π), (Mu’)(0) = (Mu’)(2π), in Lebesgue-Bochner spaces , periodic Besov spaces and periodic Triebel-Lizorkin spaces , where A and M are closed operators in a Banach space X satisfying D(A) ⊂ D(M). Our results...
Weyl almost periodic selections of supports of measure-valued functions.
Weyl product algebras and classical modulation spaces
We discuss continuity properties of the Weyl product when acting on classical modulation spaces. In particular, we prove that is an algebra under the Weyl product when p ∈ [1,∞] and 1 ≤ q ≤ min(p,p’).
Weyl transforms associated with the Riemann-Liouville operator.
Weyl-Heisenberg frame in -adic analysis
In this paper, we establish an one-to-one mapping between complex-valued functions defined on and complex-valued functions defined on -adic number field , and introduce the definition and method of Weyl-Heisenberg frame on hormonic analysis to -adic anylysis.
What is a Sobolev space for the Laguerre function systems?
We discuss the concept of Sobolev space associated to the Laguerre operator , y ∈ (0,∞). We show that the natural definition does not agree with the concept of potential space defined via the potentials . An appropriate Laguerre-Sobolev space is defined in order to achieve that coincidence. An application is given to the almost everywhere convergence of solutions of the Schrödinger equation. Other Laguerre operators are also considered.
What is van der Corput's lemma in higher dimensions?
We consider variants of van der Corput's lemma in higher dimensions.[Proceedings of the 6th International Conference on Harmonic Analysis and Partial Differential Equations, El Escorial (Madrid), 2002].
When is the last degree solution of a Bézout identity nonnegative on the interval [-1,1]?
We give conditions such that the least degree solution of a Bézout identity is nonnegative on the interval [-1,1].
Whitney covers and quasi-isometry of -averaging domains.
Whitney's extension theorem for nonquasianalytic classes of ultradifferentiable functions
Why minimax is not that pessimistic
In nonparametric statistics a classical optimality criterion for estimation procedures is provided by the minimax rate of convergence. However this point of view can be subject to controversy as it requires to look for the worst behavior of an estimation procedure in a given space. The purpose of this paper is to introduce a new criterion based on generic behavior of estimators. We are here interested in the rate of convergence obtained with some classical estimators on almost every, in the sense...
Widom factors for the Hilbert norm
Given a probability measure μ with non-polar compact support K, we define the n-th Widom factor W²ₙ(μ) as the ratio of the Hilbert norm of the monic n-th orthogonal polynomial and the n-th power of the logarithmic capacity of K. If μ is regular in the Stahl-Totik sense then the sequence has subexponential growth. For measures from the Szegő class on [-1,1] this sequence converges to some proper value. We calculate the corresponding limit for the measure that generates the Jacobi polynomials, analyze...
Wiener amalgams and summability of Fourier series.
Wiener type theorem for regular operators of bounded support
Wolff's inequality for hypersurfaces.
We extend Wolff's "local smoothing" inequality to a wider class of not necessarily conical hypersurfaces of codimension 1. This class includes surfaces with nonvanishing curvature, as well as certain surfaces with more than one flat direction. An immediate consequence is the Lp-boundedness of the corresponding Fourier multiplier operators.