Acta mathematica scientia,Series B ›› 2017, Vol. 37 ›› Issue (2): 527-538.doi: 10.1016/S0252-9602(17)30019-X

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LOCAL ESTIMATE ABOUT SCHRÖDINGER MAXIMAL OPERATOR ON H-TYPE GROUPS

Heping LIU, Hongbo ZENG   

  1. School of Mathematical Sciences, Peking University, Beijing 100871, China
  • Received:2016-01-19 Revised:2016-05-09 Online:2017-04-25 Published:2017-04-25
  • Supported by:

    The first author is supported by National Nature Science Foundation of China (11371036).

Abstract:

Let △ be full Laplacian on H-type group G.Then for every compact set D ⊆ G, a local estimate of the Schrödinger maximal operator holds,that is,

We also show that the above inequality fails when s < 1/4.

Key words: H-type group, maximal operator, fractional Schrödinger operator

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