Sobolev Space Estimates and Symbolic Calculus for Bilinear Pseudodifferential Operators
نویسندگان
چکیده
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 CoifmanMeyer 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.
منابع مشابه
Sobolev space estimates for a class of bilinear pseudodifferential operators lacking symbolic calculus
The reappearance of a sometimes called exotic behavior for linear and multilinear pseudodifferential operators is investigated. The phenomenon is shown to be present in a recently introduced class of bilinear pseudodifferential operators which can be seen as more general variable coefficient counterparts of the bilinear Hilbert transform and other singular bilinear multipliers operators. The un...
متن کاملA Bilinear Pseudodifferential Calculus
In this paper, we are interested in the construction of a bilinear pseudodifferential calculus. We define some symbolic classes which contains those of Coifman-Meyer. These new classes allow us to consider operators closely related to the bilinear Hilbert transform. We give a description of the action of our bilinear operators on Sobolev spaces. These classes also have a “nice” behavior through...
متن کاملOn the Hörmander Classes of Bilinear Pseudodifferential Operators, II
Boundedness properties for pseudodifferential operators with symbols in the bilinear Hörmander classes of sufficiently negative order are proved. The results are obtained in the scale of Lebesgue spaces, and in some cases, end-point estimates involving weak-type spaces and BMO are provided as well. From the Lebesgue space estimates, Sobolev ones are then easily obtained using functional calculu...
متن کاملOn the Hörmander Classes of Bilinear Pseudodifferential Operators
Bilinear pseudodifferential operators with symbols in the bilinear analog of all the Hörmander classes are considered and the possibility of a symbolic calculus for the transposes of the operators in such classes is investigated. Precise results about which classes are closed under transposition and can be characterized in terms of asymptotic expansions are presented. This work extends the resu...
متن کاملAn Fio Calculus for Marine Seismic Imaging, Ii: Sobolev Estimates
We establish sharp L2-Sobolev estimates for classes of pseudodifferential operators with singular symbols [27, 20] whose non-pseudodifferential (Fourier integral operator) parts exhibit two-sided fold singularities. The operators considered include both singular integral operators along curves in R2 with simple inflection points and normal operators arising in linearized seismic imaging in the ...
متن کامل