The $\theta $-bump theorem for product fractional integrals

Abstract

We extend the one parameter θ-bump theorem for fractional integrals of Sawyer and Wheeden to the setting of two parameters, as well as improving the multiparameter result of Tanaka and Yabuta for doubling weights to classical reverse doubling weights.

Fractional integration with singularity on Light-cone,I: natural setting

“…Today, it is known as Hardy-Littlewood-Sobolev inequality for fractional integral operators. Their regularity has been extensively studied over the past several decades, for example by Stein and Weiss [8], Ricci and Stein [6], Strichartz [9], Fefferman and Muckenhoupt [11], Muckenhoupt and Wheeden [12], Sawyer and Wheeden [10], Perez [13], Sawyer and Wang [14] and Wang [15]. We consider…”