Eric T. Sawyer

A characterization of two weight norm inequalities for fractional and Poisson integrals

Caracterisation de deux inegalites de normes ponderees pour les integrales fractionnaires et de Poisson. Applications aux operateurs differentiels elliptiques degeneres

Carleson measures for analytic Besov spaces

We characterize Carleson measures for the analytic Besov spaces. The problem is first reduced to a discrete question involving measures on trees which is then solved. Applications are given to multipliers for the Besov spaces and to the determination of interpolating sequences. The discrete theorem is also applied to analysis of function space on trees.

Weighted Lebesgue and Lorentz norm inequalities for the Hardy operator

Characterizations are obtained for those pairs of weight functions w, v for which the Hardy operator Tf(x) J fo f(s) ds is bounded from the Lorentz space L"s((0, oo), v dx) to LP, ((O, oo), w dx), 0 < p, q, r, s - oo. The modified Hardy operators T,f(x) = x-17Tf(x) for q real are also treated. 1. Introduction. We characterize weighted Lebesgue and Lorentz norm inequalities for the Hardy operator Tf(x) = fox f(t) dt and the modified Hardy operators T1 f(x)

Hölder continuity of weak solutions to subelliptic equations with rough coefficients

Introduction Comparisons of conditions Proof of the general subellipticity theorem Reduction of the proofs of the rough diagonal extensions of Hormanders theorem Homogeneous spaces and subrepresentation inequalities Appendix Bibliography.

Weighted norm inequalities for operators of potential type and fractional maximal functions

In this paper, we study two-weight norm inequalities for operators of potential type in homogeneous spaces. We improve some of the results given in [6] and [8] by significantly weakening their hypotheses and by enlarging the class of operators to which they apply. We also show that corresponding results of Carleson type for upper half-spaces can be derived as corollaries of those for homogeneous spaces. As an application, we obtain some necessary and sufficient conditions for a large class of weighted norm inequalities for maximal functions under various assumptions on the measures or spaces involved.

Carleson measures and interpolating sequences for Besov spaces on complex balls

Introduction A tree structure for the unit ball

Degenerate Sobolev spaces and regularity of subelliptic equations

\mathbb{B}_n

Unique continuation for Δ+ and the C. Fefferman-Phong class

in

A characterization of two weight norm inequalities for maximal singular integrals with one doubling measure

\mathbb{C}^n

Para-accretive functions, the weak boundedness property and the Tb-Theorem

Carleson measures Pointwise multipliers Interpolating sequences An almost invariant holomorphic derivative Besov spaces on trees Holomorphic Besov spaces on Bergman trees Completing the multiplier interpolation loop Appendix Bibliography.