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Session S38 - Geometric Potential Analysis

Monday, July 19, 16:40 ~ 17:10 UTC-3

Equivalent definitions of Hardy spaces on product spaces of homogeneous type and applications

Maria Cristina Pereyra

University of New Mexico, USA   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

We present an atomic decomposition valid for product Hardy spaces on spaces of homogeneous type where minimal conditions are imposed on the underlying quasi-metric and measure. The Hardy spaces in this context were introduced by co-authors Han, Li and Ward using square functions based on orthogonal wavelet bases of Auscher and Hytönen and underlying reference dyadic grids on the spaces of homogeneous type. This decomposition enables us to show that the product Hardy spaces and their duals (the Carleson Measure Spaces, including BMO and VMO) are independent of the Auscher-Hytönen wavelets chosen and the Hytönen-Kairema dyadic cubes the wavelet are based on.

Joint work with Yongsheng Han (Auburn University, USA), Ji Li (Macquarie University, Australia) and Lesley Ward (University of South Australia, Australia).

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