Analysis Mathematica

, Volume 39, Issue 4, pp 287–296 | Cite as

Sharp inequalities for geometric maximal operators associated with general measures

  • Adam Osękowski


We determine the best constants in the weak-type (p, p) and L p estimates for geometric maximal operator on (ℝ, µ). It is also shown that in higher dimensions such inequalities fail to hold.


Lebesgue Measure General Measure Good Constant Weight Norm Inequality Sharp Inequality 
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Неулучшаемые неравенства для геометрических максимальных операторов, связанных с общими мерами


В работе установлены неулучшаемые значения констант в неравенствах слабого типа (p, p) и в L p -оценках для геометрического максимального оператора на (ℝ, µ). Показано, что в случае более высокой размерности подобные оценки неверны.


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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2013

Authors and Affiliations

  1. 1.Department of Mathematics, Informatics and MechanicsUniversity of WarsawWarsawPoland

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