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

Kabe Moen — 2009

Studia Mathematica

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 and the...

Mixed A p - A ∞ estimates with one supremum

Andrei K. Lerner;  Kabe Moen — 2013

Studia Mathematica

We establish several mixed A p - A ∞ bounds for Calderón-Zygmund operators that only involve one supremum. We address both cases when the A ∞ part of the constant is measured using the exponential-logarithmic definition and using the Fujii-Wilson definition. In particular, we answer a question of the first author and provide an answer, up to a logarithmic factor, to a conjecture of Hytönen and Lacey. Moreover, we give an example to show that our bounds with the logarithmic factors can be arbitrarily smaller...

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