In this paper, we develop via real variable methods various characterisations of the Hardy spaces in the multi-parameter flag setting. These characterisations include those via, the non-tangential and radial maximal function, the Littlewood-Paley square function and area integral, Riesz transforms and the atomic decom-position in the multi-parameter flag setting. The novel ingredients in this paper include (1) establishing appropriate discrete Calder???on reproducing formulae in the flag setting and a version of the ...
Read More
In this paper, we develop via real variable methods various characterisations of the Hardy spaces in the multi-parameter flag setting. These characterisations include those via, the non-tangential and radial maximal function, the Littlewood-Paley square function and area integral, Riesz transforms and the atomic decom-position in the multi-parameter flag setting. The novel ingredients in this paper include (1) establishing appropriate discrete Calder???on reproducing formulae in the flag setting and a version of the Plancherel-P???olya inequalities for flag quadratic forms; (2) introducing the maximal function and area function via flag Poisson kernels and flag version of harmonic functions; (3) developing an atomic decom-position via the finite speed propagation and area function in terms of flag heat semigroups. As a consequence of these real variable methods, we obtain the full characterisations of the multi-parameter Hardy space with the flag structure.
Read Less
Add this copy of Maximal Functions, Littlewood-Paley Theory, Riesz to cart. $91.19, new condition, Sold by Paperbackshop rated 4.0 out of 5 stars, ships from Bensenville, IL, UNITED STATES, published 2022 by American Mathematical Society.
Add this copy of Maximal Functions, Littlewood-Paley Theory, Riesz to cart. $106.84, new condition, Sold by Booksplease rated 4.0 out of 5 stars, ships from Southport, MERSEYSIDE, UNITED KINGDOM, published 2022 by American Mathematical Society.
Add this copy of Maximal Functions, Littlewood-Paley Theory, Riesz to cart. $121.08, new condition, Sold by Revaluation Books rated 4.0 out of 5 stars, ships from Exeter, DEVON, UNITED KINGDOM, published 2022 by Amer Mathematical Society.
