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Register a new userOn a Problem of Jaak Peetre Concerning Pointwise Multipliers of Besov Spaces
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We characterize the set of all pointwise multipliers of the Besov spaces $B^s_{p,q}(R)$ under the restrictions $0 < p,q le infty$ and $s>d/p$.
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We continue our investigations on pointwise multipliers for Besov spaces of dominating mixed smoothness. This time we study the algebra property of the classes $S^r_{p,q}B(mathbb{R}^d)$ with respect to pointwise multiplication. In addition if $pleq q$, we are able to describe the space of all pointwise multipliers for $S^r_{p,q}B(mathbb{R}^d)$.
Let $X$ be a space of homogeneous type and let $L$ be a nonnegative self-adjoint operator on $L^2(X)$ which satisfies a Gaussian estimate on its heat kernel. In this paper we prove a Homander type spectral multiplier theorem for $L$ on the Besov and Triebel--Lizorkin spaces associated to $L$. Our work not only recovers the boundedness of the spectral multipliers on $L^p$ spaces and Hardy spaces associated to $L$, but also is the first one which proves the boundedness of a general spectral theorem on Besov and Triebel--Lizorkin spaces.
This paper is devoted to giving definitions of Besov spaces on an arbitrary open set of $mathbb R^n$ via the spectral theorem for the Schrodinger operator with the Dirichlet boundary condition. The crucial point is to introduce some test function spaces on $Omega$. The fundamental properties of Besov spaces are also shown, such as embedding relations and duality, etc. Furthermore, the isomorphism relations are established among the Besov spaces in which regularity of functions is measured by the Dirichlet Laplacian and the Schrodinger operators.
In this article we examine Dirichlet type spaces in the unit polydisc, and multipliers between these spaces. These results extend the corresponding work of G. D. Taylor in the unit disc. In addition, we consider functions on the polydisc whose restrictions to lower dimensional polydiscs lie in the corresponding Dirichet type spaces. We see that such functions need not be in the Dirichlet type space of the whole polydisc. Similar observations are made regarding multipliers.
We study the embeddings of (homogeneous and inhomogeneous) anisotropic Besov spaces associated to an expansive matrix $A$ into Sobolev spaces, with focus on the influence of $A$ on the embedding behaviour. For a large range of parameters, we derive sharp characterizations of embeddings.
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