Semi-groupes holomorphes et -convexité (suite)
Semilinear Poisson problems in Sobolev-Besov spaces on Lipschitz domains.
Extending recent work for the linear Poisson problem for the Laplacian in the framework of Sobolev-Besov spaces on Lipschitz domains by Jerison and Kenig [16], Fabes, Mendez and Mitrea [9], and Mitrea and Taylor [30], here we take up the task of developing a similar sharp theory for semilinear problems of the type Δu - N(x,u) = F(x), equipped with Dirichlet and Neumann boundary conditions.
Semiorthogonal linear prewavelets on irregular meshes
We extend results on constructing semiorthogonal linear spline prewavelet systems in one and two dimensions to the case of irregular dyadic refinement. In the one-dimensional case, we obtain sharp two-sided inequalities for the -condition, 1 < p < ∞, of such systems.
Séries de Fourier et séries d'ondelettes
Series expansions for Fourier transforms and Lebesgue functions
Series trigonometriques speciales et corps quadratiques
Sets of Divergence of Fourier Series.
Sets of Uniform Convergence and Strong Riesz Sets.
Sets of uniqueness
Sets of -expansions and the Hausdorff measure of slices through fractals
We study natural measures on sets of -expansions and on slices through self similar sets. In the setting of -expansions, these allow us to better understand the measure of maximal entropy for the random -transformation and to reinterpret a result of Lindenstrauss, Peres and Schlag in terms of equidistribution. Each of these applications is relevant to the study of Bernoulli convolutions. In the fractal setting this allows us to understand how to disintegrate Hausdorff measure by slicing, leading...
Shannon wavelets theory.
Shannon's sampling theorem, incongruent residue classes and Plancherel's theorem
Sampling theory for multi-band signals is shown to have a logical structure similar to that of Fourier analysis.
Shape functions and wavelets - tools of numerical approximation
Solution of a boundary value problem is often realized as the application of the Galerkin method to the weak formulation of given problem. It is possible to generate a trial space by means of splines or by means of functions that are not polynomial and have compact support. We restrict our attention only to RKP shape functions and compactly supported wavelets. Common features and comparison of approximation properties of these functions will be studied in the contribution.
Sharp and weighted inequalities for multilinear integral operators.
In this paper, we prove some weighted inequalities for the multilinear operators related to certain integral operators on the generalized Morrey spaces by using the sharp estimates of the multilinear operators. The operators include Littlewood-Paley operator, Marcinkiewicz operator and Bochner-Riesz operator.
Sharp endpoint results for imaginary powers and Riesz transforms on certain noncompact manifolds
We consider a complete connected noncompact Riemannian manifold M with bounded geometry and spectral gap. We prove that the imaginary powers of the Laplacian and the Riesz transform are bounded from the Hardy space X¹(M), introduced in previous work of the authors, to L¹(M).
Sharp Estimates for Commutators of Singular Integrals via Iterations of the Hardy-Littlewood Maximal Function.
Sharp estimates of the Jacobi heat kernel
The heat kernel associated with the setting of the classical Jacobi polynomials is defined by an oscillatory sum which cannot be computed explicitly, in contrast to the situation for the other two classical systems of orthogonal polynomials. We deduce sharp estimates giving the order of magnitude of this kernel, for type parameters α, β ≥ -1/2. Using quite different methods, Coulhon, Kerkyacharian and Petrushev recently also obtained such estimates. As an application of the bounds, we show that...
Sharp function estimate for multilinear commutator of Littlewood-Paley operator
Sharp function estimate for multilinear commutator of singular integral with variable Calderón-Zygmund kernel.
Sharp Function Inequalities and Boundness for Toeplitz Type Operator Related to General Fractional Singular Integral Operator