Representation of bi-parameter singular integrals by dyadic operators
By Henri Martikainen. 2011
80 citations recorded by the source corpus.
Abstract We prove a dyadic representation theorem for bi-parameter singular integrals. That is, we represent certain bi-parameter operators as averages of rapidly decaying sums of what we call bi-parameter shifts. A new version of the product space T 1 theorem is established as a consequence.
Subfields: Applied Mathematics
View Paper: https://www.semanticscholar.org/paper/3117db2b82cdb1d075f71d37ad42dd778bb9283d
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In Applied Mathematics
- Brett D. Wick
- Tuomas Hytönen
- I. Holmes
- Andrei K. Lerner
- S. Petermichl
- Michael T. Lacey
- D. Cruz-Uribe
- Kabe Moen
Citations in the corpus
- Representation of singular integrals by dyadic operators, and the A_2 theorem (2011, methodology): “[8] Tuomas Hytönen, Michael T. Lacey, Henri Martikainen, Tuomas Orponen, Maria Carmen Reguera, Eric T. Sawyer, and Ignacio Uriarte-Tuero.”
- Weighted little bmo and two-weight inequalities for Journé commutators (2017, methodology): “Section 6 is dedicated to biparameter paraproducts, which will be crucial in the final Section 7, which proves the upper bound by an appeal to Martikainen’s [14] representation theorem.”