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

100%

Martell J.

Studia Mathematica

2004

tom 161

nr 2

113-145

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.

Generalized Hörmander conditions and weighted endpoint estimates

51%

Lorente M., Martell J., Pérez C., Riveros M.

Studia Mathematica

2009

tom 195

nr 2

157-192

We consider two-weight estimates for singular integral operators and their commutators with bounded mean oscillation functions. Hörmander type conditions in the scale of Orlicz spaces are assumed on the kernels. We prove weighted weak-type estimates for pairs of weights (u,Su) where u is an arbitrary nonnegative function and S is a maximal operator depending on the smoothness of the kernel. We also obtain sufficient conditions on a pair of weights (u,v) for the operators to be bounded from $L^{p}(v)$ to $L^{p,∞}(u)$. One-sided singular integrals, like the differential transform operator, are considered as well. We also provide applications to Fourier multipliers and homogeneous singular integrals.

Ograniczanie wyników

2 Studia Mathematica

2 Martell J.

1 Lorente M.

1 Pérez C.

1 Riveros M.

1 2009

1 2004

Wyniki wyszukiwania

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

Generalized Hörmander conditions and weighted endpoint estimates