Sharp weak type inequalities for the dyadic maximal operator
Eleftherios Nikolidakis
TL;DR
This paper derives precise bounds for the distribution of the dyadic maximal operator applied to functions in Lp, based on L1 and Lq norms, under specific weak Lp conditions.
Contribution
It provides sharp localized distribution estimates for the dyadic maximal operator with new bounds involving L1, Lq norms, and weak Lp conditions.
Findings
Established sharp bounds for the dyadic maximal operator
Connected distribution estimates to L1, Lq norms and weak Lp conditions
Enhanced understanding of maximal operator behavior in localized settings
Abstract
We obtain sharp estimates for the localized distribution function of M\phi, when \phi belongs to Lp,\inf where M is the dyadic maximal operator. We obtain these estimates given the L1 and Lq norm, q < p and certain weak Lp-conditions.
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Taxonomy
TopicsAdvanced Harmonic Analysis Research · Differential Equations and Boundary Problems · Holomorphic and Operator Theory