Maximal operator for pseudo-differential operators with homogeneous symbols

Details Maximal operator for pseudo-differential operators with homogeneous symbols Maximal operator for pseudo-differential operators with homogeneous symbols

2008-09-13

arxiv.org/abs/0809.2313v1

Mathematics

Functional Analysis

22 pages

Scientific paper

The aim of the present paper is to obtain a Sj\"{o}lin-type maximal estimate for pseudo-differential operators with homogeneous symbols. The crux of the proof is to obtain a phase decomposition formula which does not involve the time traslation. The proof is somehow parallel to the paper by Pramanik and Terwilleger (P. Malabika and E. Terwilleger, A weak $L^2$ estimate for a maximal dyadic sum operator on $R^n$, Illinois J. Math, {\bf 47} (2003), no. 3, 775--813). In the present paper, we mainly concentrate on our new phase decomposition formula and the results in the Cotlar type estimate, which are different from the ones by Pramanik and Terwilleger.

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