An abstract theory of singular operators

Abstract

We introduce a class of operators on abstract measure spaces, which unifies the Calderón-Zygmund operators on spaces of homogeneous type, the maximal functions and the martingale transforms. We prove that such operators can be dominated by simple sparse operators with a definite form of the domination constant. Applying these estimates, we improve several results obtained by different authors in recent years.

accepted in Transactions of the AMS

References in corpus (2)

• On pointwise estimates involving sparse operators
• Sharp Reverse Hölder property for A_\infty weights on spaces of homogeneous type

Cited by in corpus (9)

• Maximal polynomial modulations of singular integrals
• A class of multilinear bounded oscillation operators on measure spaces and applications
• A metric approach to sparse domination
• On good-$\lambda$ inequalities for couples of measurable functions
• On almost everywhere convergence of Malmquist-Takenaka series
• On pointwise ${\ell }^r$-sparse domination in a space of homogeneous type
• Bounded oscillation operators on BMO spaces
• On a weak type estimate for sparse operators of strong type
• Maximal operators on spaces BMO and BLO