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March  2005, 4(1): 45-91. doi: 10.3934/cpaa.2005.4.45

Maximal function estimates with applications to a modified Kadomstev-Petviashvili equation

C. E. Kenig 1, and  S. N. Ziesler 2,

1. 

Department of Mathematics, University of Chicago, IL 60637, United States
2. 

Department of Mathematics and Computer Science, Dominican University, River Forest, IL 60305, United States

Received  February 2004 Revised  August 2004 Published  December 2004

In this paper we give optimal (up to endpoint) maximal function type estimates for the solution of the linear initial value problem associated with the Kadomstev-Petviashvili I equation. These estimates enable us to obtain a well-posedness result for a modified Kadomstev-Petviashvili I equation.
Keywords: Kadomstev-Petviashvili., maximal function estimates.
Mathematics Subject Classification: 35Q53, 42B2.
Citation: C. E. Kenig, S. N. Ziesler. Maximal function estimates with applications to a modified Kadomstev-Petviashvili equation. Communications on Pure and Applied Analysis, 2005, 4 (1) : 45-91. doi: 10.3934/cpaa.2005.4.45
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