On the precise asymptotics of the constant in Friedrich's inequality for functions vanishing on the part of the boundary with microinhomogeneous structure.
We prove that, for certain domains , continuous product of domains , the Carathéodory pseudodistance satisfies the following product property
This paper studies a new maximal operator introduced by Hytönen, McIntosh and Portal in 2008 for functions taking values in a Banach space. The -boundedness of this operator depends on the range space; certain requirements on type and cotype are present for instance. The original Euclidean definition of the maximal function is generalized to σ-finite measure spaces with filtrations and the -boundedness is shown not to depend on the underlying measure space or the filtration. Martingale techniques...
Let denote the non-quasianalytic class of Beurling type on an open set Ω in . For the surjectivity of the convolution operator is characterized by various conditions, e.g. in terms of a convexity property of the pair and the existence of a fundamental solution for μ or equivalently by a slowly decreasing condition for the Fourier-Laplace transform of μ. Similar conditions characterize the surjectivity of a convolution operator between ultradistributions of Roumieu type whenever . These...
We study the regularity properties of bilinear maximal operator. Some new bounds and continuity for the above operators are established on the Sobolev spaces, Triebel-Lizorkin spaces and Besov spaces. In addition, the quasicontinuity and approximate differentiability of the bilinear maximal function are also obtained.
In this paper we study the regularity properties of the one-dimensional one-sided Hardy-Littlewood maximal operators and . More precisely, we prove that and map with , boundedly and continuously. In addition, we show that the discrete versions and map boundedly and map continuously. Specially, we obtain the sharp variation inequalities of and , that is, if , where is the total variation of on and is the set of all functions satisfying .