Generalized weighted Sobolev spaces and applications to Sobolev orthogonal polynomials: a survey.
Generating new classes of orthogonal polynomials.
Generating some semiclassical orthogonal polynomials.
Geodesics in the Heisenberg Group
We provide a new and elementary proof for the structure of geodesics in the Heisenberg group Hn. The proof is based on a new isoperimetric inequality for closed curves in R2n.We also prove that the Carnot- Carathéodory metric is real analytic away from the center of the group.
Geometric and approximation properties of some singular integrals in the unit disk.
Geometric Fourier analysis
In this paper we continue the study of the Fourier transform on , , analyzing the “almost-orthogonality” of the different directions of the space with respect to the Fourier transform. We prove two theorems: the first is related to an angular Littlewood-Paley square function, and we obtain estimates in terms of powers of , where is the number of equal angles considered in . The second is an extension of the Hardy-Littlewood maximal function when one consider cylinders of , , of fixed eccentricity...
Gibbs' Phenomenon and Arclength.
Gibbs' Phenomenon for Sampling Series and What To Do About It.
Gibbs Phenomenon on Sampling Series Based on Shannon's and Meyer's Wavelet Analysis.
Global behavior of integral transforms.
Global estimates for singular integrals of the composition of the maximal operator and the Green's operator.
Global higher integrability of jacobians on bounded domains
Global integrability of the Jacobian of a composite mapping.
Global maximal estimates for solutions to the Schrödinger equation
Global maximal estimates are considered for solutions to an initial value problem for the Schrödinger equation.
Global mild solutions of the micropolar fluid system in critical spaces
We prove the global in time existence of a small solution for the 3D micropolar fluid system in critical Fourier-Herz spaces by using the Fourier localization method and Littlewood-Paley theory.
Global orthogonality implies local almost-orthogonality.
We introduce a new stopping-time argument, adapted to handle linear sums of noncompactly-supported functions that satisfy fairly weak decay, smoothness, and cancellation conditions. We use the argument to obtain a new Littlewood-Paley-type result for such sums.
Global well-posedness for KdV in Sobolev spaces of negative index.
Global well-posedness for the 2-D Boussinesq system with temperature-dependent thermal diffusivity
We prove the global well-posedness of the 2-D Boussinesq system with temperature dependent thermal diffusivity and zero viscosity coefficient.
Good λ inequalities for the area integral and the nontangential maximal function
Good-λ inequalities for wavelets of compact support
For a wavelet ψ of compact support, we define a square function and a maximal function NΛ. We then obtain the equivalence of these functions for 0 < p < ∞. We show this equivalence by using good-λ inequalities.