Radial variation in some function spaces

Radial Variation of Functions in Besov Spaces

Abstract This paper considers the radial variation function F (r, t) of an analytic function f(z) on the disc D. We examine F (r, t) when f belongs to a Besov space Apq and look for ways in which F imitates the behaviour of f . Regarded as a function of position (r, t) in D, we show that F obeys a certain integral growth condition which is the real variable analogue of that satisfied by f . We ...

compactifications and function spaces on weighted semigruops

chapter one is devoted to a moderate discussion on preliminaries, according to our requirements. chapter two which is based on our work in (24) is devoted introducting weighted semigroups (s, w), and studying some famous function spaces on them, especially the relations between go (s, w) and other function speces are invesigated. in fact this chapter is a complement to (32). one of the main fea...

Radial Maximal Function Characterizations for Hardy Spaces on RD-spaces

An RD-space X is a space of homogeneous type in the sense of Coifman and Weiss with the additional property that a reverse doubling property holds. The authors prove that for a space of homogeneous type X having “dimension” n, there exists a p0 ∈ (n/(n+ 1), 1) such that for certain classes of distributions, the L(X ) quasi-norms of their radial maximal functions and grand maximal functions are ...

Radial Basis Function Interpolation in Sobolev Spaces and Its Applications

In this paper we study the method of interpolation by radial basis functions and give some error estimates in Sobolev space H(Ω) (k ≥ 1). With a special kind of radial basis function, we construct a basis in H(Ω) and derive a meshless method for solving elliptic partial differential equations. We also propose a method for computing the global data density. Mathematics subject classification: 41...

The Isometries of Some Function Spaces