arXiv subjects

Theresa C. Anderson

Publications and source records attributed to Theresa C. Anderson.

39 records · Page 3Linked to original sources

arXiv2014

Calderón-Zygmund operators and commutators in spaces of homogeneous type: weighted inequalities

The recent proof of the sharp weighted bound for Calderón-Zygmund operators has led to much investigation in sharp mixed bounds for operators and commutators, that is, a sharp weighted bound that is a product of at least two different $A_p$ weight constants. The reason why these are sought after is that the product will be strictly smaller than the original one-constant bound. We prove a variety of these bounds in spaces of homogeneous type, using the new techniques of Lerner, for both operators and commutators.

math.CA↗

arXiv2013

Logarithmic bump conditions for Calderón-Zygmund Operators on spaces of homogeneous type

We establish two-weight norm inequalities for singular integral operators defined on spaces of homogeneous type. We do so first when the weights satisfy a double bump condition and then when the weights satisfy separated logarithmic bump conditions. Our results generalize recent work on the Euclidean case, but our proofs are simpler even in this setting. The other interesting feature of our approach is that we are able to prove the separated bump results (which always imply the corresponding double bump results) as a consequence of the double bump theorem.

math.CA↗

arXiv2012

A simple proof of the sharp weighted estimate for Calderon-Zygmund operators on homogeneous spaces

Here we show that Lerner's method of local mean oscillation gives a simple proof of the $A_2$ conjecture for spaces of homogeneous type: that is, the linear dependence on the $A_2$ norm for weighted $L^2$ Calderon-Zygmund operator estimates. In the Euclidean case, the result is due to Hytönen, and for geometrically doubling spaces, Nazarov, Rezinikov, and Volberg obtained the linear bound.

math.CA↗