Hardy Spaces of Differential Forms on Riemannian Manifolds

Abstract

Abstract. Let M be a complete connected Riemannian manifold. Assuming that the Riemannian measure is doubling, we define Hardy spaces H p of differential forms on M and give various characterizations of them, including an atomic decomposition. As a consequence, we derive the H p -boundedness for Riesz transforms on M, generalizing previously known results. Further applications, in particular to H ∞ functional calculus and Hodge decomposition, are given.

Sharp endpoint results for imaginary powers and Riesz transforms on certain noncompact manifolds

“…follows from [AMR,Theorem 5.13] and that of the imaginary powers from [DY,Corollary 4.3]. However, we believe that the proofs outlined here might be of some interest for their simplicity.…”

Maximal function characterizations for Hardy spaces associated with nonnegative self-adjoint operators on spaces of homogeneous type

“…In this case, we can choose b (3) and a (4) to be any positive number. For example, we let b (3) = b (1) and a (4) = a (2) . (4) and a (5) be any positive number.…”

“…For the theory of Hardy spaces associated to operators, it has attracted a lot of attention in the last decades, and has been a very active research topic in harmonic analysis -see for example, [1,2,3,7,10,11,12,13,15,16,17,18,21,23,24].…”

“…We now recall the notion of a (p, q, M)-atom associated to an operator L ( [2,11,15]). The atomic Hardy space H p L,at,q,M (X) is defined as follows.…”

Herz-Type Hardy Spaces Associated with Operators

“…Yang and his cooperators discussed new Orlicz-Hardy spaces associated with operators [10][11][12][13]. For more results, we refer to [14][15][16][17][18][19] and the references therein.…”