On $A_p$-$A_{\infty }$ type estimates for square functions

Abstract

We prove strong-type $A_p$-$A_{\infty }$ estimate for square functions, improving on the $A_p$ bound due to Lerner. Entropy bounds, in the recent innovation of Treil-Volberg, are then proved. The techniques of proof include parallel stopping cubes, pigeon-hole arguments, and the approach to entropy bounds of Lacey--Spencer.

12 pages. Final version, to appear in Math. Z

References in corpus (3)

• Two weight norm inequalities for the $g$ function
• Another proof of Scurry's characterization of a two weight norm inequality for a sequence-valued positive dyadic operator
• Mixed $A_p$-$A_r$ inequalities for classical singular integrals and Littlewood-Paley operators

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• On pointwise ${\ell }^r$-sparse domination in a space of homogeneous type
• Intrinsic square functions with arbitrary aperture