Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
  1. Home
  2. Search

Refine search

Refine search

Access:
Content type:
Publication date:
Apply   From and To filters
Subject: Show more
Journals Show more
Publishers: Show more
Societies Show more
Series: Show more
Collections: Show more

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

1 results

  • 8 - Convolution and Beyond

  • Albert Baernstein II, Washington University, St Louis
  • Book:
    Symmetrization in Analysis
    Published online:
    22 February 2019
    Print publication:
    14 March 2019, pp 254-298

  • Summary

    Chapter 8 studies symmetrization and convolution.The Riesz-Sobolev convolution theorem is first proved for functions in the unit circle, and then the real line, and finally in n-dimensional space. The Brunn-Minkowski inequality is proved as an application. The Brascamp-LIeb-Luttinger inequality, which extends the Riesz-Sobolev inequality to multiple integrals,is proved too. It implies that the Dirichlet heat kernel increases under symmetrization of the domain.The chapter includes a variation of the sharp Hardy-Littlewood-Sobolev inequality that implies Beckner's logarithmic Sobolev inequality. The latter result is used to establish hypercontractivity of the Poisson semigroup.