Multidimensional van der Corput and sublevel set estimates
نویسندگان
چکیده
منابع مشابه
Multidimensional Van Der Corput and Sublevel Set Estimates
If a function has a large derivative, then it changes rapidly, and so spends little time near any particular value. This paper is devoted to quantifying that principle for functions of several variables, particularly as it pertains to two problems in harmonic analysis. Along the way we shall encounter diverse problems and techniques, and shall be led to issues distinctly combinatorial in nature...
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1. Sublevel set estimates The importance of sublevel set estimates in van der Corput lemmas was highlighted by A. Carbery, M. Christ, and J. Wright [3], [4]. We find the sharp constant in the following sublevel set estimate. We will use this in Section 4 to prove an asymptotically sharp van der Corput lemma. The constants Cn take different values in each lemma. Lemma 1. Suppose that f : (a, b) ...
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ژورنال
عنوان ژورنال: Journal of the American Mathematical Society
سال: 1999
ISSN: 0894-0347,1088-6834
DOI: 10.1090/s0894-0347-99-00309-4