Sparse bounds for maximal monomial oscillatory Hilbert transforms

作者：Krause Ben^*; Lacey Michael T

来源：Studia Mathematica, 2018, 242(3): 217-229.

DOI：10.4064/sm8699-7-2017

• maximal truncation
• Hilbert transform
• sparse bound

For each d >= 2, the maximal truncation of the Hilbert transform with a polynomial oscillation,
H(*)f(x) = sup (epsilon) vertical bar integral(vertical bar y vertical bar > epsilon) f(x - y) e(2 pi iyd)/y dy vertical bar,
satisfies a (1,r) sparse bound for all r > 1. This quickly implies weak-type inequalities for the maximal truncations, which hold for A l weights, but are new even in the case of Lebesgue measure. The unweighted weak-type estimate without maximal truncations but with arbitrary polynomials is due to Chanillo and Christ (1987).

• 出版日期2018