John E. Gilbert

Learn More
In memory of A. P. Calderón ×ØÖÖغ This paper proves the L p-boundedness of general bilinear operators associated to a symbol or multiplier which need not be smooth. The Main Theorem establishes a general result for multipliers that are allowed to have singularities along the edges of a cone as well as possibly at its vertex. It thus unifies ealier results(More)
This thesis is dedicated to my mother and the greatest influence on my life, Late Mrs. Sushil Monga Acknowledgments I would like to begin by thanking my parents, albeit I understand any amount of gratitude shown to them is woefully inadequate. My father's unconditional support is largely the reason that this PhD is completed in United States. No words are(More)
The study of bilinear operators associated to a class of non-smooth symbols can be reduced to the study of certain special bilinear cone operators to which a time frequency analysis using smooth wave-packets is performed. In this paper we prove that when smooth wave-packets are replaced by Walsh wave-packets the corresponding discrete Walsh model for the(More)
In memory of A. P. Calderón ×ØÖÖغ This paper completes the proof of the L p-boundedness of bilinear operators associated to nonsmooth symbols or multipliers begun in Part I, our companion paper [8], by establishing the corresponding L p-boundedness of time-frequency paraproducts associated with tiles in phase plane. The affine invariant structure of such(More)
A relation between the Bilinear Hilbert transform and triangular truncations of Hankel and Toeplitz operators is established. Boundedness of triangular truncations of Han-kel operators then follows from deep, known properties for the Bilinear Hilbert transform, connrming a conjecture attributed to Peller. These properties also provide a uniied alternative(More)
The Hardy space H 1 ρr (R n) consists of all divergence free r-form distributions f whose non-tangential maximal functions are in L 1 (R n). We say that a system of singular integrals characterizes H 1 ρr (R n) if this space consists precisely of those divergence-free r-form distributions f whose images under the singular integral operators are integrable.(More)
  • 1