Print Email Facebook Twitter Even Fourier multipliers and martingale transforms in infinite dimensions Title Even Fourier multipliers and martingale transforms in infinite dimensions Author Yaroslavtsev, I.S. (TU Delft Analysis) Date 2018 Abstract In this paper we show sharp lower bounds for norms of even homogeneous Fourier multipliers in L(Lp(Rd;X)) for 1<p<∞and for a UMD Banach space X in terms of the range of the corresponding symbol. For example, if the range contains a1,…,aN∈C, then the norm of the multiplier exceeds ‖a1R1 2+⋯+aNRN 2‖L(Lp(RN;X)), where Rn is the corresponding Riesz transform. We also provide sharp upper bounds of norms of Bañuelos–Bogdan type multipliers in terms of the range of the functions involved. The main tools that we exploit are A-weak differential subordination of martingales and UMDp A constants, which are introduced here. Subject Even Fourier multipliersMartingale transformsUMD Banach spacesWeak differential subordination To reference this document use: http://resolver.tudelft.nl/uuid:13423e77-cf5b-4fa0-be1a-0e809e1426f9 DOI https://doi.org/10.1016/j.indag.2018.05.014 Embargo date 2020-09-13 ISSN 0019-3577 Source Indagationes Mathematicae, 29 (5), 1290-1309 Bibliographical note Accepted Author Manuscript Part of collection Institutional Repository Document type journal article Rights © 2018 I.S. Yaroslavtsev Files PDF 45503696_Yaroslavtsev.pdf 509.19 KB Close viewer /islandora/object/uuid:13423e77-cf5b-4fa0-be1a-0e809e1426f9/datastream/OBJ/view