Shaoming Guo

activity

20142026

most citedMaximal operators and Hilbert transforms along variable non-flat homogeneous curves

35 citations · 210 across the 41 of their papers we have counts for

collaborators

Showing 2015Show all

3 papers · 1 filter

math.CA2015

A geometric proof of Bourgain's $L^{2}$ estimate of maximal operators along analytic vector fields

Shaoming Guo

Bourgain proved that the maximal operator associated to an analytic vector field is bounded on $L^{2}$ . In the present paper, we give a geometric proof of Bourgain's result by using…

math.CA2015

Remarks on the maximal operator and Hilbert transform along variable parabolas

Shaoming Guo

We prove the boundedness of the maximal operator and Hilbert transform along certain variable parabolas in $L^{p}$ for $p > p_{0}$ with some $p_{0} \in (1, 2)$ . Connections with the Hilbert…

math.CA2015

Oscillatory integrals related to Carleson's theorem: fractional monomials

Shaoming Guo

Stein and Wainger proved the $L^{p}$ bounds of the polynomial Carleson operator for all integer-power polynomials without linear term. In the present paper, we partially generalise t…

A geometric proof of Bourgain's L2 estimate of maximal operators along analytic vector fields

Remarks on the maximal operator and Hilbert transform along variable parabolas

Oscillatory integrals related to Carleson's theorem: fractional monomials

A geometric proof of Bourgain's $L^{2}$ estimate of maximal operators along analytic vector fields