Two weight inequalities for certain maximal fractional operators on spaces of homogeneous type

In this paper we prove sharp weighted BMO estimates for singular integrals, and we show how such estimates can be extrapolated to Banach function spaces1. © 2022

In applying the density of finite sums of atoms, we are not making use of the finite atomic decomposition norm (as in Theorem 2.6 for weighted spaces or in the corresponding result

Introduction Proof of the T(P) Theorem A geometric condition for the Beurling transform.. A T(1) theorem for Sobolev spaces

Finally, weincludean appendix with a proof of the John-Nirenberg theorem on spaces of homogeneous type, because it is not easy to find in the literature a proof for the Lebesgue

We show that embeddings for restricted non-linear approximation spaces in terms of weighted Lorentz sequence spaces are equivalent to Jackson and Bernstein type inequalities, and

In Chapter 2, our aim is to develop the regularity theory of Holder spaces adapted to L and to study estimates of operators like fractional integrals L −σ/ 2 , and fractional powers

Theorem 2. For the corresponding evolution operators one can prove similar Carleman-type inequalities with sharp weights that capture the natural boundary conditions and the natural L

The proof relies on an integral representation of the fractional Laplace-Beltrami operator on a general compact manifold and an instantaneous continuity result for weak solutions