Sobolev space estimates and symbolic calculus for bilinear pseudodifferential operators |
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Authors: | Árpád Bényi Andrea R Nahmod Rodolfo H Torres |
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Institution: | 1. Department of Mathematics, Western Washington University, 516 High St, 98225, Bellingham, WA 2. Department of Mathematics and Statistics, University of Massachusetts, Lederle GRT, 01003, Amherst, MA 3. Department of Mathematics, University of Kansas, 66045, Lawrence, KS
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Abstract: | Bilinear operators are investigated in the context of Sobolev spaces and various techniques useful in the study of their boundedness
properties are developed. In particular, several classes of symbols for bilinear operators beyond the so-called Coifman-Meyer
class are considered. Some of the Sobolev space estimates obtained apply to both the bilinear Hilbert transform and its singular
multipliers generalizations as well as to operators with variable dependent symbols. A symbolic calculus for the transposes
of bilinear pseudodifferential operators and for the composition of linear and bilinear pseudodifferential operators is presented
too. |
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Keywords: | |
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