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

100%

Moen K.

Studia Mathematica

2009

tom 194

nr 2

163-180

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 testing condition of Sawyer. Finally, our approach leads to a new proof of Buckley's sharp estimate for the Hardy-Littlewood maximal function.

Mixed $A_{p}-A_{∞}$ estimates with one supremum

63%

Lerner A., Moen K.

Studia Mathematica

2013

tom 219

nr 3

247-267

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 than the previously known bounds (both with one supremum and two suprema).

Ograniczanie wyników

2 Studia Mathematica

2 Moen K.

1 Lerner A.

1 2013

1 2009

Wyniki wyszukiwania

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

Mixed $A_{p}-A_{∞}$ estimates with one supremum