Leslie Cheng

BOUNDEDNESS OF ROUGH INTEGRAL OPERATORS ON TRIEBEL-LIZORKIN SPACES

We prove the boundedness of several classes of rough integral operators on Triebel-Lizorkin spaces. Our results represent improvements as well as natural extensions of many previously known results.

Logarithmic Bounds for Oscillatory Singular Integrals on Hardy Spaces

We establish a logarithmic bound for oscillatory singular integrals with quadratic phases on the Hardy space . The logarithmic rate of growth is the best possible.

Weighted Estimates for Oscillatory Singular Integrals

We establish uniform bounds for oscillatory singular integrals as well as oscillatory singular integral operators. We allow the singular kernel to be given by a function in the Hardy space , while such results were known previously only for kernels in log , a proper subspace of . One of our results established a bound for certain weights. At the same time, it provides a solution to an open problem in Lu (2005).