Sharp maximal functions associated with approximations of the identity in spaces of homogeneous type and applications

José María Martell. "Sharp maximal functions associated with approximations of the identity in spaces of homogeneous type and applications." Studia Mathematica 161.2 (2004): 113-145. <http://eudml.org/doc/285331>.

@article{JoséMaríaMartell2004,
abstract = {In the context of the spaces of homogeneous type, given a family of operators that look like approximations of the identity, new sharp maximal functions are considered. We prove a good-λ inequality for Muckenhoupt weights, which leads to an analog of the Fefferman-Stein estimate for the classical sharp maximal function. As a consequence, we establish weighted norm estimates for certain singular integrals, defined on irregular domains, with Hörmander conditions replaced by some estimates which do not involve the regularity of the kernel. We apply these results to prove the boundedness of holomorphic functional calculi on Lebesgue spaces with Muckenhoupt weights. In particular, some applications are given to second order elliptic operators with different boundary conditions.},
author = {José María Martell},
journal = {Studia Mathematica},
keywords = {singular integrals; Muckenhoupt weights; sharp maximal functions; spaces of homogeneous type; holomorphic calculi; semigroup kernels; elliptic operators},
language = {eng},
number = {2},
pages = {113-145},
title = {Sharp maximal functions associated with approximations of the identity in spaces of homogeneous type and applications},
url = {http://eudml.org/doc/285331},
volume = {161},
year = {2004},
}

TY - JOUR
AU - José María Martell
TI - Sharp maximal functions associated with approximations of the identity in spaces of homogeneous type and applications
JO - Studia Mathematica
PY - 2004
VL - 161
IS - 2
SP - 113
EP - 145
AB - In the context of the spaces of homogeneous type, given a family of operators that look like approximations of the identity, new sharp maximal functions are considered. We prove a good-λ inequality for Muckenhoupt weights, which leads to an analog of the Fefferman-Stein estimate for the classical sharp maximal function. As a consequence, we establish weighted norm estimates for certain singular integrals, defined on irregular domains, with Hörmander conditions replaced by some estimates which do not involve the regularity of the kernel. We apply these results to prove the boundedness of holomorphic functional calculi on Lebesgue spaces with Muckenhoupt weights. In particular, some applications are given to second order elliptic operators with different boundary conditions.
LA - eng
KW - singular integrals; Muckenhoupt weights; sharp maximal functions; spaces of homogeneous type; holomorphic calculi; semigroup kernels; elliptic operators
UR - http://eudml.org/doc/285331
ER -