Intrinsic Square Function Characterizations of Hardy Spaces with Variable Exponents

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 ...

New real-variable characterizations of Hardy spaces associated with twisted convolution

Intrinsic Characterizations of Tangent Spaces

Given a real Cx structure ionaC" manifold containing a point P, the tangent space Tp is exactly the linear space Ep of all linear maps A^>DR such that Dfg = iPf)Dg + iPg)Df for (/, g)£AXA, i.e., the space of P-derivations of A. However, if A is a C structure for r < °o then £p is much larger than Tp (see [2] and [3]). Our purpose is to introduce a coordinate-free characterization of Tp which is...

Intrinsic atomic characterizations of function spaces on domains

Radial maximal function characterizations of Hardy spaces on RD-spaces and their applications

Let X be an RD-space with μ(X ) = ∞, which means that X is a space of homogeneous type in the sense of Coifman and Weiss and its measure has the reverse doubling property. In this paper, we characterize the atomic Hardy spaces H at(X ) of Coifman and Weiss for p ∈ (n/(n + 1), 1] via the radial maximal function, where n is the “dimension” of X , and the range of index p is the best possible. Thi...