Maximal operator for pseudo-differential operators with homogeneous symbols
نویسنده
چکیده
The aim of the present paper is to obtain a Sjölin-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 L2 estimate for a maximal dyadic sum operator on Rn, Illinois J. Math, 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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