6,502 research outputs found
Representation of bi-parameter singular integrals by dyadic operators
We prove a dyadic representation theorem for bi-parameter singular integrals.
That is, we represent certain bi-parameter operators as rapidly decaying
averages of what we call bi-parameter shifts. A new version of the product
space T1 theorem is established as a consequence.Comment: 26 page
Vector-valued non-homogeneous Tb theorem on metric measure spaces
We prove a vector-valued non-homogeneous Tb theorem on certain quasimetric
spaces equipped with what we call an upper doubling measure. Essentially, we
merge recent techniques from the domain and range side of things, achieving a
Tb theorem which is quite general with respect to both of them.Comment: 31 page
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