II L p - BOUNDEDNESS FOR TIME - FREQUENCY PARAPRODUCTS , II
نویسندگان
چکیده
This paper completes the proof of the Lp-boundedness of bilinear operators associated to nonsmooth symbols or multipliers begun in Part I, our companion paper [8], by establishing the corresponding Lp-boundedness of time-frequency paraproducts associated with tiles in phase plane. The affine invariant structure of such operators in conjunction with the geometric properties of the associated phase-plane decompositions allow Littlewood-Paley techniques to be applied locally, ie. on trees. Boundedness of the full time-frequency paraproduct then follows using ‘almost orthogonality’ type arguments relying on estimates for tree-counting functions together with decay estimates.
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