A matrix weighted bilinear Carleson lemma and maximal function
(2019) In Analysis and Mathematical Physics Abstract
We prove a bilinear Carleson embedding theorem with matrix weight and scalar measure. In the scalar case, this becomes exactly the well known weighted bilinear Carleson embedding theorem. Although only allowing scalar Carleson measures, it is to date the only extension to the bilinear setting of the recent Carleson embedding theorem by Culiuc and Treil that features a matrix Carleson measure and a matrix weight. It is well known that a Carleson embedding theorem implies a Doob’s maximal inequality and this holds true in the matrix weighted setting with an appropriately defined maximal operator. It is also known that a dimensional growth must occur in the Carleson embedding theorem with matrix Carleson measure, even with trivial weight.... (More)
We prove a bilinear Carleson embedding theorem with matrix weight and scalar measure. In the scalar case, this becomes exactly the well known weighted bilinear Carleson embedding theorem. Although only allowing scalar Carleson measures, it is to date the only extension to the bilinear setting of the recent Carleson embedding theorem by Culiuc and Treil that features a matrix Carleson measure and a matrix weight. It is well known that a Carleson embedding theorem implies a Doob’s maximal inequality and this holds true in the matrix weighted setting with an appropriately defined maximal operator. It is also known that a dimensional growth must occur in the Carleson embedding theorem with matrix Carleson measure, even with trivial weight. We give a definition of a maximal type function whose norm in the matrix weighted setting does not grow with dimension.
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 author
 Petermichl, Stefanie; Pott, Sandra ^{LU} and Reguera, Maria Carmen
 organization
 publishing date
 20190627
 type
 Contribution to journal
 publication status
 epub
 subject
 in
 Analysis and Mathematical Physics
 external identifiers

 scopus:85068326795
 ISSN
 16642368
 DOI
 10.1007/s13324019003319
 language
 English
 LU publication?
 yes
 id
 a6e869aad11f4e88802d88b5f601289e
 date added to LUP
 20190711 16:33:24
 date last changed
 20190711 16:33:24
@article{a6e869aad11f4e88802d88b5f601289e, abstract = {<p>We prove a bilinear Carleson embedding theorem with matrix weight and scalar measure. In the scalar case, this becomes exactly the well known weighted bilinear Carleson embedding theorem. Although only allowing scalar Carleson measures, it is to date the only extension to the bilinear setting of the recent Carleson embedding theorem by Culiuc and Treil that features a matrix Carleson measure and a matrix weight. It is well known that a Carleson embedding theorem implies a Doob’s maximal inequality and this holds true in the matrix weighted setting with an appropriately defined maximal operator. It is also known that a dimensional growth must occur in the Carleson embedding theorem with matrix Carleson measure, even with trivial weight. We give a definition of a maximal type function whose norm in the matrix weighted setting does not grow with dimension.</p>}, author = {Petermichl, Stefanie and Pott, Sandra and Reguera, Maria Carmen}, issn = {16642368}, language = {eng}, month = {06}, series = {Analysis and Mathematical Physics}, title = {A matrix weighted bilinear Carleson lemma and maximal function}, url = {http://dx.doi.org/10.1007/s13324019003319}, year = {2019}, }