In this paper we overview known and recently obtained results on Morrey-Campanato
spaces with respect to the properties of the spaces themselves, that is, we do not touch the …

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 …

We work on RD-spaces 𝒳, namely, spaces of homogeneous type in the sense of Coifman
and Weiss with the additional property that a reverse doubling property holds in 𝒳. An …

Consider a second order divergence form elliptic operator L with complex bounded
measurable coefficients. In general, operators based on L, such as the Riesz transform or …

[1] Alexopoulos G., An application of homogeneization theory to harmonic analysis: Harnack
inequalities and Riesz transforms on Lie groups of polynomial growth, Canad. J. Math. 44 …

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 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 …

Let be a metric space with doubling measure, L a nonnegative self-adjoint operator in
satisfying the Davies–Gaffney estimate, ω a concave function on (0,∞) of strictly lower type …