This article unifies the theory for Hardy spaces built on Banach lattices on ${\mathbb {R}}^ n
$ satisfying certain weak conditions on indicator functions of balls. The authors introduce a …

Let $ X $ be a metric space with doubling measure, and $ L $ be a non-negative, self-adjoint
operator satisfying Davies-Gaffney bounds on $ L^ 2 (X) $. In this article we present a theory …

Let $ L $ be the infinitesimal generator of an analytic semigroup on $ L^ 2 ({\mathbb R}^ n) $
with suitable upper bounds on its heat kernels. Auscher, Duong, and McIntosh defined a …

In this paper, we introduce and develop some new function spaces of BMO (bounded mean
oscillation) type on spaces of homogeneous type or measurable subsets of spaces of …

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 …

Let A be an n× n matrix with entries (1.1) ajk: Rn−→ C, j= 1,..., n, k= 1,..., n, satisfying the
ellipticity condition (1.2) λ| ξ| 2≤ eAξ· ξ and| Aξ· ζ|≤ Λ| ξ|| ζ|,∀ ξ, ζ∈ Cn, for some constants …

Let L be the divergence form elliptic operator with complex bounded measurable
coefficients, ω the positive concave function on (0,∞) of strictly critical lower type pω∈(0, 1] …

We show various L p estimates for Schrödinger operators−∆+ V on Rn and their square
roots. We assume reverse Hölder estimates on the potential, and improve some results of …

Let M be a complete, noncompact Riemannian manifold, µ the Riemannian measure,∇ the
Riemannian gradient, and the (positive) Laplace-Beltrami operator on M. Denote by|·| the …

We investigate Fourier multipliers on the compact dual of arbitrary discrete groups. Our main
result is a Hörmander–Mihlin multiplier theorem for finite-dimensional cocycles with optimal …