On the bilinear Hilbert transform along two polynomials
نویسندگان
چکیده
منابع مشابه
On the Two Dimensional Bilinear Hilbert Transform
We investigate the Bilinear Hilbert Transform in the plane and the pointwise convergence of bilinear averages in Ergodic theory, arising from Z actions. Our techniques combine novel one and a half dimensional phase-space analysis with more standard one dimensional theory.
متن کاملOn the Bilinear Hilbert Transform
In joint work with C. Thiele, the author has shown that A. Calderón’s bilinear Hilbert transform extends to a bounded operator on certain products of L spaces. This article illustrates the method of proof by giving a complete proof of an inequality which is slightly weaker than the original conjecture of Calderón concerning this transform. 1991 Mathematics Subject Classification: 42A50
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متن کاملDistributional Estimates for the Bilinear Hilbert Transform
We obtain size estimates for the distribution function of the bilinear Hilbert transform acting on a pair of characteristic functions of sets of finite measure, that yield exponential decay at infinity and blowup near zero to the power −2/3 (modulo some logarithmic factors). These results yield all known L bounds for the bilinear Hilbert transform and provide new restricted weak type endpoint e...
متن کاملThe bilinear Hilbert transform acting on Hermite and Laguerre functions
We obtain several formulas for the action of the bilinear Hilbert transform on pairs of Hermite and Laguerre functions. The result can be expressed as a linear combination of products of Hermite or Laguerre functions.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2019
ISSN: 0002-9939,1088-6826
DOI: 10.1090/proc/14518