Bernstein's theorem on weighted Besov spaces.
Besicovitch Type Maximal Operators and Applications to Fourier Analysis.
Besov-type spaces on R and integrability for the Dunkl transform.
Best approximations for the Laguerre-type Weierstrass transform on .
Beurling-Hörmander uncertainty principle for the spherical mean operator.
Bilinear multipliers on Lorentz spaces
We give one sufficient and two necessary conditions for boundedness between Lebesgue or Lorentz spaces of several classes of bilinear multiplier operators closely connected with the bilinear Hilbert transform.
Bochner-Hecke Theorems for the Weinstein Transform and Application
MSC 2010: 42B10, 44A15In this paper we prove Bochner-Hecke theorems for the Weinstein transform and we give an application to homogeneous distributions.
Boundedness of singular integral operators with holomorphic kernels on star-shaped closed Lipschitz curves
The aim of this paper is to study singular integrals T generated by holomorphic kernels defined on a natural neighbourhood of the set , where is a star-shaped Lipschitz curve, . Under suitable conditions on F and z, the operators are given by (1) We identify a class of kernels of the stated type that give rise to bounded operators on . We establish also transference results relating the boundedness of kernels on closed Lipschitz curves to corresponding results on periodic, unbounded curves.
C1 Changes of Variable: Beurling-Helson Type Theorem and Hörmander Conjecture on Fourier Multipliers.
Clifford algebras, Fourier transforms and singular convolution operators on Lipschitz surfaces.
In the Fourier theory of functions of one variable, it is common to extend a function and its Fourier transform holomorphically to domains in the complex plane C, and to use the power of complex function theory. This depends on first extending the exponential function eixξ of the real variables x and ξ to a function eizζ which depends holomorphically on both the complex variables z and ζ .Our thesis is this. The natural analog in higher dimensions is to extend a function of m real variables monogenically...
Conditional Fourier-Feynman transform given infinite dimensional conditioning function on abstract Wiener space
We study a conditional Fourier-Feynman transform (CFFT) of functionals on an abstract Wiener space . An infinite dimensional conditioning function is used to define the CFFT. To do this, we first present a short survey of the conditional Wiener integral concerning the topic of this paper. We then establish evaluation formulas for the conditional Wiener integral on the abstract Wiener space . Using the evaluation formula, we next provide explicit formulas for CFFTs of functionals in the Kallianpur...
Confirmation of Matheron's conjecture on the covariogram of a planar convex body
Continuous wavelet transform on semisimple Lie groups and inversion of the Abel transform and its dual.
In this work we define and study wavelets and continuous wavelet transform on semisimple Lie groups G of real rank l. We prove for this transform Plancherel and inversion formulas. Next using the Abel transform A on G and its dual A*, we give relations between the continuous wavelet transform on G and the classical continuous wavelet transform on Rl, and we deduce the formulas which give the inverse operators of the operators A and A*.
Convergence a.e. of spherical partial Fourier integrals on weighted spaces for radial functions: endpoint estimates
We prove some extrapolation results for operators bounded on radial functions with p ∈ (p₀,p₁) and deduce some endpoint estimates. We apply our results to prove the almost everywhere convergence of the spherical partial Fourier integrals and to obtain estimates on maximal Bochner-Riesz type operators acting on radial functions in several weighted spaces.
Corrigendum of Mean Quadratic Variations and Fourier Asymptotics of Self-similar Measures.
Damping oscillatory integrals.
Darstellung temperierter vektorwertiger Distributionen durch holomorphe Funktionen II.
Differential operators of gradient type associated with spherical harmonics
Dispersion Phenomena in Dunkl-Schrödinger Equation and Applications
2000 Mathematics Subject Classification: 35Q55,42B10.In this paper, we study the Schrödinger equation associated with the Dunkl operators, we study the dispersive phenomena and we prove the Strichartz estimates for this equation. Some applications are discussed.