Asset Details
Do you wish to reserve the book?
A Short Proof of the Uniform Smoothness of Certain Lebesgue Spaces
Hey, we have placed the reservation for you!
By the way, why not check out events that you can attend while you pick your title.
Oops! Something went wrong.
Looks like we were not able to place the reservation. Kindly try again later.
Are you sure you want to remove the book from the shelf?
A Short Proof of the Uniform Smoothness of Certain Lebesgue Spaces
Do you wish to request the book?
A Short Proof of the Uniform Smoothness of Certain Lebesgue Spaces
Please be aware that the book you have requested cannot be checked out. If you would like to checkout this book, you can reserve another copy
We have requested the book for you!
Your request is successful and it will be processed during the Library working hours. Please check the status of your request in My Requests.
Oops! Something went wrong.
Looks like we were not able to place your request. Kindly try again later.
Journal Article
A Short Proof of the Uniform Smoothness of Certain Lebesgue Spaces
2020
Overview
This note gives a short, direct proof of the uniform smoothness of L
p
spaces with
. Current proofs in the literature use the uniform convexity of the L
p
spaces and the duality between convexity and smoothness. As a corollary, using duality, we obtain the uniform convexity of the L
p
spaces with
, which is the notoriously \"difficult\" range, without recourse to Clarkson's second inequality. The method of proof also gives the power-type of the modulus of smoothness of L
p
spaces with
; this is known and was stated by J. Lindenstrauss and L. Tzafriri in Classical Banach Spaces II in Chapter 1, Section e. The proof was postponed to Vol. III, but this was never written.
Publisher
Taylor & Francis,Taylor & Francis, Ltd
Subject
