Two-weight norm inequalities for maximal functions on homogeneous spaces and boundary estimates

Sérgio Zani

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Displaying similar documents to “Two-weight norm inequalities for maximal functions on homogeneous spaces and boundary estimates”

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

José María Martell (2004)

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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...

Sharp one-weight and two-weight bounds for maximal operators

Kabe Moen (2009)

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We investigate the boundedness of the fractional maximal operator with respect to a general basis on weighted Lebesgue spaces. We characterize the boundedness of these operators for one-weight and two-weight inequalities extending the work of Jawerth. A new two-weight testing condition for the fractional maximal operator on a general basis is introduced extending the work of Sawyer for the basis of cubes. We also find the sharp dependence in the two-weight case between the operator norm...

Maximal functions and related weight classes.

Carlo Sbordone, Ingemar Wik (1994)

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The famous result of Muckenhoupt on the connection between weights w in A-classes and the boundedness of the maximal operator in L(w) is extended to the case p = ∞ by the introduction of the geometrical maximal operator. Estimates of the norm of the maximal operators are given in terms of the A-constants. The equality of two differently defined A-constants is proved. Thereby an answer is given to a question posed by R. Johnson. For non-increasing functions on the positive real line a...

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Notes on Retracts of Coset Spaces

J. van Mill, G. J. Ridderbos (2005)

Bulletin of the Polish Academy of Sciences. Mathematics

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We study retracts of coset spaces. We prove that in certain spaces the set of points that are contained in a component of dimension less than or equal to n, is a closed set. Using our techniques we are able to provide new examples of homogeneous spaces that are not coset spaces. We provide an example of a compact homogeneous space which is not a coset space. We further provide an example of a compact metrizable space which is a retract of a homogeneous compact space, but which is not...

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Distances between Hilbertian operator spaces

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We compute the completely bounded Banach-Mazur distance between different finite-dimensional homogeneous Hilbertian operator spaces.

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We characterize geometric properties of a family of approach regions by means of analytic properties of the class of weights related to the boundedness of the maximal operator associated with this family.