Related papers: Sharp radial estimates in Besov spaces

We develop a theory of bounded variation functions and Besov spaces in abstract Dirichlet spaces which unifies several known examples and applies to new situations, including fractals.

We obtain new improved spectral projection estimates on manifolds of non-positive curvature, including sharp ones for relatively large spectral windows for general tori. Our results are stronger than those in an earlier work of the first…

We prove a sharp Lp estimate for a singular Radon transform according to a size condition of its kernel, which is useful for extrapolation.

In this paper the authors obtain a new equivalent norms of the Besov spaces of variable smoothness and integrability. Our main tools are the continuous version of Calderon reproducing formula, maximal inequalities and variable exponent…

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 Schr\"odinger operator with the Dirichlet boundary condition. The crucial point is to introduce some test…

We discuss supernear spaces.

We develop an approximation theory in Hilbert spaces that generalizes the classical theory of approximation by entire functions of exponential type. The results advance harmonic analysis on manifolds and graphs, thus facilitating data…

We prove sharp uniqueness results for a wide class of one-dimensional discrete evolutions. The proof is based on a construction from the theory of complex Jacobi matrices combined with growth estimates of entire functions.

Under certain restrictions we describe the set of all pointwise multipliers in case of Sobolev and Besov spaces of dominating mixed smoothness. In addition we shall give necessary and sufficient conditions for the case that these spaces…

The paper considers estimates for some sums and products of functions of prime numbers. Several assertions on this topic have been proven. We also study extremal estimates for strongly additive and strongly multiplicative arithmetic…

For an interpolation pair $(E_0,E_1)$ of Banach spaces with $E_1 \hookrightarrow E_0$ we use vectors $b_1,b_2,\ldots \in E_1$ that satisfy an extremal property with respect to the $J$- and $K$-functional to construct sub-spaces that are…

We estimate the norm of the harmonic Bergman projection in the context of harmonic Besov spaces. We obtain the two-side norm estimates in general Lp-case.

We obtain (essentially sharp) boundedness results for certain generalized local maximal operators between fractional weighted Sobolev spaces and their modifications. Concrete boundedness results between well known fractional Sobolev spaces…

We establish conditions on the parameters which are both necessary and sufficient in order that Besov and Triebel-Lizorkin spaces of generalized smoothness contain only regular distributions. We also connect this with the possibility of…

We use the method of pseudoanalytic continuation to obtain a characterization of spaces of holomorphic functions with boundary values in Besov spaces in terms of polynomial approximations.

We study fractional Sobolev and Besov spaces on noncompact Riemannian manifolds with bounded geometry. Usually, these spaces are defined via geodesic normal coordinates which, depending on the problem at hand, may often not be the best…

Recently, Kulikov (\cite{Ku}) has shown that certain convex functionals on weighted Bergman spaces are maximized by reproducing kernels. We show a sharp quantitative stability of these estimates with the optimal norm and the exponent and an…

We develop a set of techniques that enable us to effectively recover Besov rough analysis from p-variation rough analysis. Central to our approach are new metric groups, in which some objects in rough path theory that have been previously…

We give characterizations for homogeneous and inhomogeneous Besov-Lizorkin-Triebel spaces in terms of continuous local means for the full range of parameters. In particular, we prove characterizations in terms of Lusin functions and spaces…

We note a sharp embedding of the Besov space $B^\infty_{0,q}(\bbT)$ into exponential classes and prove entropy estimates for the compact embedding of subclasses with logarithmic smoothness, considered by Kashin and Temlyakov.