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Inequalities for L^p-norms that sharpen the triangle inequality and complement Hanner's Inequality

Carlen, Eric A. and Frank, Rupert L. and Ivanisvili, Paata and Lieb, Elliott H. (2018) Inequalities for L^p-norms that sharpen the triangle inequality and complement Hanner's Inequality. . (Unpublished) http://resolver.caltech.edu/CaltechAUTHORS:20190520-141054764

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Abstract

In 2006 Carbery raised a question about an improvement on the naïve norm inequality ∥f+g∥^p_p ≤ 2^(p−1)(∥f∥^p_p+∥g∥^p_p) for two functions in L^p of any measure space. When f=g this is an equality, but when the supports of f and g are disjoint the factor 2^(p−1) is not needed. Carbery's question concerns a proposed interpolation between the two situations for p>2. The interpolation parameter measuring the overlap is ∥fg∥_(p/2). We prove an inequality of this type that is stronger than the one Carbery proposed. Moreover, our stronger inequalities are valid for all p.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/1807.05599arXivDiscussion Paper
ORCID:
AuthorORCID
Carlen, Eric A.0000-0003-2613-187X
Frank, Rupert L.0000-0001-7973-4688
Lieb, Elliott H.0000-0001-5843-3587
Additional Information:© 2018 by the authors. This paper may be reproduced, in its entirety, for non-commercial purposes. Work partially supported by NSF grants DMS-1501007 (E.A.C.), DMS-1363432 (R.L.F.), PHY-1265118 (E.H.L.).
Funders:
Funding AgencyGrant Number
NSFDMS-1501007
NSFDMS-1363432
NSFPHY-1265118
Record Number:CaltechAUTHORS:20190520-141054764
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20190520-141054764
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:95611
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:20 May 2019 23:17
Last Modified:20 May 2019 23:17

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