Annales Academię Scientiarum Fennicę
Mathematica
Volumen 38, 2013, 229-244

OPTIMAL WEAK TYPE ESTIMATES FOR DYADIC-LIKE MAXIMAL OPERATORS

Eleftherios N. Nikolidakis

University of Crete, Department of Mathematics
Heraklion 71409, Crete, Greece; lefteris 'at' math.uoc.gr

Abstract. We provide sharp weak estimates for the distribution function of M\phi when on \phi we impose L¹, L^q and L^p,\infty restrictions. Here M\phi is the dyadic maximal operator associated to a tree T on a non-atomic probability measure space. As a consequence we produce that the inequality ||M\phi_T\phi||_p,\infty \le |||\phi|||_p,\infty is sharp allowing every possible value for the L¹ and the L^q norm for a fixed q such that 1 < q < p, where |||\cdot|||_p,\infty is the integral norm on and ||\cdot||_p,\infty the usual quasi norm on L^p,\infty.

2010 Mathematics Subject Classification: Primary 47A30.

Key words: Dyadic, maximal.

Reference to this article: E.N. Nikolidakis: Optimal weak type estimates for dyadic-like maximal operators. Ann. Acad. Sci. Fenn. Math. 38 (2013), 229-244.

Full document as PDF file

doi:10.5186/aasfm.2013.3817

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