Endpoint bounds for multilinear fractional integrals

Strong Type Endpoint Bounds for Analytic Families of Fractional Integrals

In R2, we consider an analytic family of fractional integrals , whose convolution kernel is obtained by taking some transverse derivatives of arclength measure on the parabola (t, t2) multiplied by |t|γ , and doing so in a homogeneous way. We determine the exact range of p, q for which the analytic family maps Lp to Lq . We also resolve a similar issue on the Heisenberg group.

Bounds for Singular Fractional Integrals and Related Fourier Integral Operators

Bounds for Multilinear Sublevel Sets

The question in the form (1.2) was posed by Li, Tao, Thiele, and this author in [5]. Nonoscillatory inequalities of the form ∫ ∏ j |fj◦`j | . ∏ j ‖fj‖Lpj have been studied in [1],[2]. Oscillatory integral inequalities of this type have been extensively studied for n = 2, where one is dealing with bilinear forms 〈Tλ(f1), f2〉. The associated linear operators Tλ are commonly known as oscillatory i...

Weighted Inequalities on Morrey Spaces for Linear and Multilinear Fractional Integrals with Homogeneous Kernels

In this paper, we consider weighted inequalities for linear and multilinear fractional integrals with homogeneous kernels on Morrey spaces. Recently, weighted inequalities without homogeneous kernels were proved by the authors. In this paper, we generalize ones with homogeneous kernels.

Multilinear Calderón–zygmund Singular Integrals

This paper contains the material covered in a minicourse given by the author at the Centre de Recerca Matemàtica in Barcelona during the period May 4–9, 2009. The course was an expanded version of a series of three lectures delivered by the author two weeks earlier (April 23–25) at the New Mexico Analysis Seminar held at the University of New Mexico in Albuquerque. The author would like to than...