The Convergence in L... of Singular Integrals in Harmonic Analysis and Ergodic Theory.
The dual of Hardy spaces on a bounded domain in Rn.
The Dunkl transform.
The Ehrhart polynomial of a lattice -simplex.
The fall of the doubling condition in Calderón-Zygmund theory.
The most important results of standard Calderón-Zygmund theory have recently been extended to very general non-homogeneous contexts. In this survey paper we describe these extensions and their striking applications to removability problems for bounded analytic functions. We also discuss some of the techniques that allow us to dispense with the doubling condition in dealing with singular integrals. Special attention is paid to the Cauchy Integral.[Proceedings of the 6th International Conference on...
The form boundedness criterion for the relativistic Schrödinger operator
We establish necessary and sufficient conditions on the real- or complex-valued potential defined on for the relativistic Schrödinger operator to be bounded as an operator from the Sobolev space to its dual .
The Fourier integral operators on Hardy spaces associated with Herz spaces
In this paper, it is proved that the Fourier integral operators of order , with , are bounded from three kinds of Hardy spaces associated with Herz spaces to their corresponding Herz spaces.
The Fourier transform in weighted Lorenz spaces.
The Fourier transforms of Lipschitz functions on certain domains.
The fractional integral between weighted Orlicz and spaces on spaces of homogeneous type
In this work we give sufficient and necessary conditions for the boundedness of the fractional integral operator acting between weighted Orlicz spaces and suitable spaces, in the general setting of spaces of homogeneous type. This result generalizes those contained in [P1] and [P2] about the boundedness of the same operator acting between weighted and Lipschitz integral spaces on . We also give some properties of the classes of pairs of weights appearing in connection with this boundedness.
The fractional maximal operator and fractional integrals on variable spaces.
The fundamental solution for a consistent complex model of the shallow shell equations.
The fundamental solution of a modified Oseen problem.
The Green formula and HP Spaces on trees.
The Hardy-Lorentz spaces
We deal with the Hardy-Lorentz spaces where 0 < p ≤ 1, 0 < q ≤ ∞. We discuss the atomic decomposition of the elements in these spaces, their interpolation properties, and the behavior of singular integrals and other operators acting on them.
The Hausdorff operators on the real Hardy spaces
We prove that the Hausdorff operator generated by a function ϕ is bounded on the real Hardy space , 0 < p ≤ 1, if the Fourier transform ϕ̂ of ϕ satisfies certain smoothness conditions. As a special case, we obtain the boundedness of the Cesàro operator of order α on , 2/(2α+1) < p ≤ 1. Our proof is based on the atomic decomposition and molecular characterization of .
The higher order Riesz transform for Gaussian measure need not be of weak type (1,1)
The purpose of this paper is to prove that the higher order Riesz transform for Gaussian measure associated with the Ornstein-Uhlenbeck differential operator , x ∈ ℝ, need not be of weak type (1,1). A function in , where dγ is the Gaussian measure, is given such that the distribution function of the higher order Riesz transform decays more slowly than C/λ.
The Hilbert transform and maximal function along nonconvex curves in the plane.
In this paper we study the Hilbert transform and maximal function related to a curve in R2.
The Hilbert transform in weighted spaces of integrable vector-valued functions
The inner periodic structure of a function.