Title: Morrey spaces: introduction and applications to integral operators and PDE's/Yoshihiro
Sawano, Giuseppe Di Fazio, Denny Ivanal Hakim. Description: First edition.| Boca Raton …

The Solution of the Kato Square Root Problem for Second Order Elliptic Operators on Rⁿ
Page 1 Annals of Mathematics, 156 (2002), 633-654 The solution of the Kato square root …

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 …

This is a survey on recent developments of the theory of one-parameter semigroups and
evolution equations with special emphasis on functional calculus and kernel estimates. Also …

We prove quadratic estimates for complex perturbations of Dirac-type operators, and thereby
show that such operators have a bounded functional calculus. As an application we show …

We consider divergence form elliptic operators $ L={-}\mathrm {div} A (x)\nabla $, defined in
the half space $\mathbb {R}^{n+ 1} _+ $, $ n\geq 2$, where the coefficient matrix $ A (x) $ is …

The theory of Carleson measures, stopping time arguments, and atomic decompositions has
been well-established in harmonic analysis. More recent is the theory of phase space …

We consider divergence form elliptic operators of the form L=− divA (x)∇, defined in Rn+
1={(x, t)∈ Rn× R}, n⩾ 2, where the L∞ coefficient matrix A is (n+ 1)×(n+ 1), uniformly elliptic …

Abstract Let E⊂ ℝ n+ 1, n≥ 2, be an Ahlfors–David regular set of dimension n. We show
that the weak-A∞ property of harmonic measure, for the open set Ω:= ℝ n+ 1∖ E, implies …

We prove the Kato conjecture for elliptic operators and N× N-systems in divergence form of
arbitrary order 2 m on \BbbR^n. More precisely, we assume the coefficients to be bounded …