Hardy--Littlewood fractional maximal operators on homogeneous trees
Matteo Levi, Federico Santagati
TL;DR
This paper investigates the behavior of Hardy--Littlewood fractional maximal operators on homogeneous trees, focusing on their mapping properties between Lorentz spaces and establishing the optimality of these results.
Contribution
It provides new insights into the boundedness and optimality of fractional maximal operators on homogeneous trees, extending classical results to this setting.
Findings
Characterized the boundedness of fractional maximal operators between Lorentz spaces.
Proved the optimality of the obtained mapping results.
Extended classical Euclidean space results to homogeneous trees.
Abstract
We study the mapping properties of the Hardy--Littlewood fractional maximal operator between Lorentz spaces of the homogeneous tree and discuss the optimality of all the results.
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Taxonomy
TopicsAdvanced Harmonic Analysis Research · Nonlinear Partial Differential Equations · Advanced Mathematical Physics Problems