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arXiv · 2001.11546

On the endpoint behaviour of oscillatory maximal function

Tainara Borges·Cynthia Bortolotto·João P. G. Ramos
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Abstract

Inspired by a question of Lie, we study boundedness in subspaces of $L^1(\mathbb{R})$ of oscillatory maximal functions. In particular, we construct functions in $L^1(\mathbb{R})$ which are never integrable under action of our class of maximal functions. On the other hand, we prove that these maximal functions map certain classes of spaces resembling Sobolev spaces into $L^1(\mathbb{R})$ continuously under mild curvature assumptions on the phase $\gamma$.

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Tainara Borges, Cynthia Bortolotto, João P. G. Ramos. 2020-01-30. On the endpoint behaviour of oscillatory maximal function. https://arxiv.org/abs/2001.11546

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