相关论文: Bilinear estimates in Besov spaces generated by th…
In the whole space $\mathbb R^d$, linear estimates for heat semi-group in Besov spaces are well established, which are estimates of $L^p$-$L^q$ type, maximal regularity, e.t.c. This paper is concerned with such estimates for semi-group…
We study $L^p$ Besov critical exponents and isoperimetric and Sobolev inequalities associated with fractional Laplacians on metric measure spaces. The main tool is the theory of heat semigroup based Besov classes in Dirichlet spaces that…
We revisit the problem of obtaining uniform gradient estimates for Dirichlet and Neumann heat semigroups on Riemannian manifolds with boundary. As applications, we obtain isoperimetric inequalities, using Ledoux's argument, and uniform…
In this paper we prove characterizations of the discrete Besov spaces in terms of the heat and Poisson semigroups associated with the discrete Laplacian that will allow us to prove regularity results for the fractional powers of the…
In this paper, we establish Brezin-Li-Yau type lower bounds for averaged sums of Dirichlet eigenvalues of the Laplacian and poly-Laplacian on bounded domains in Euclidean spaces. By deriving expansions of two binary polynomials which may be…
We study the bilinear estimates in the Sobolev spaces with the Dirichlet and the Neumann boundary condition. The optimal regularity is revealed to get such estimates in the half space case, which is related to not only smoothness of…
This note shows the existence of a sharp bilinear estimate for the Bourgain-type space and gives its application to the optimal local well/ill-posedness of the Cauchy problem for the Benjamin equation.
Wavelet bases and frames consisting of band limited functions of nearly exponential localization on Rd are a powerful tool in harmonic analysis by making various spaces of functions and distributions more accessible for study and…
Using the framework of a previous article joint with Axelsson and McIntosh, we extend to systems two results of S. Hofmann for real symmetric equations and their perturbations going back to a work of B. Dahlberg for Laplace's equation on…
We prove sharp bilinear estimates for Dirichlet or Neumann eigenfunctions in domains in the plane. These are the natural analog of earlier estimates for the boundaryless case of Burq, G\'erard, and Tzvetkov.
This paper is devoted to the study of gradient estimates for the Dirichlet problem of the heat equation in the exterior domain of a compact set. Our results describe the time decay rates of the derivatives of solutions to the Dirichlet…
The purpose of this paper is to give a definition and prove the fundamental properties of Besov spaces generated by the Neumann Laplacian. As a by-product of these results, the fractional Leibniz rule in these Besov spaces is obtained.
This paper provides sharp Dirichlet heat kernel estimates in inner uniform domains, including bounded inner uniform domains, in the context of certain (possibly non-symmetric) bilinear forms resembling Dirichlet forms. For instance, the…
We describe a procedure to introduce Sobolev spaces and the semigroup generated by the fractional Dirichlet Laplacian on an arbitrary domain of $\R^d$. In particular, the well-definedness of the spaces of both non-homogeneous and…
We introduce heat semigroup-based Besov classes in the general framework of Dirichlet spaces. General properties of those classes are studied and quantitative regularization estimates for the heat semigroup in this scale of spaces are…
In this paper we present certain bilinear estimates for commutators on Besov spaces with variable smoothness and integrability, and under no vanishing assumptions on the divergence of vector fields. Such commutator estimates are motivated…
Multilinear embedding estimates for the fractional Laplacian are obtained in terms of functionals defined over a hyperbolic surface. Convolution estimates used in the proof enlarge the classical framework of the convolution algebra for…
We compute three-term semiclassical asymptotic expansions of counting functions and Riesz-means of the eigenvalues of the Laplacian on spheres and hemispheres, for both Dirichlet and Neumann boundary conditions. Specifically for Riesz-means…
We introduce the class of bounded variation (BV) functions in a general framework of strictly local Dirichlet spaces with doubling measure. Under the 2-Poincar\'e inequality and a weak Bakry-\'Emery curvature type condition, this BV class…
We compute the norm of some bilinear forms on products of weighted Besov spaces in terms of the norm of their symbol in a space of pointwise multipliers defined in terms of Carleson measures.