Search

Skip to main content Accessibility help

Home
Search

Only show content I have access to (0)

Articles (1)

Over 3 years (1)

From year:

To year:

Apply

fractional maximal functions

Proceedings of the London Mathematical Society (1)

View selected items
Save to my bookmarks
Export citations
Download PDF (zip)
Save to Kindle
Save to Dropbox
Save to Google Drive
Save content to
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to .

To save content items to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Please be advised that item(s) you selected are not available.
You are about to save
Your Kindle email address

Please provide your Kindle email.

@free.kindle.com @kindle.com (service fees apply)

By using this service, you agree that you will only keep content for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services

1 results

SHARP GEOMETRIC POINCARÉ INEQUALITIES FOR VECTOR FIELDS AND NON-DOUBLING MEASURES
BRUNO FRANCHI, CARLOS PÉREZ, RICHARD L. WHEEDEN
Journal:

Proceedings of the London Mathematical Society / Volume 80 / Issue 3 / May 2000

Published online by Cambridge University Press:

20 August 2001, pp. 665-689

Print publication:

May 2000
- Article
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation
We derive Sobolev--Poincaré inequalities that estimate the $L^q(d\mu)$ norm of a function on a metric ball when $\mu$ is an arbitrary Borel measure. The estimate is in terms of the $L^1(d\nu)$ norm on the ball of a vector field gradient of the function, where $d\nu/dx$ is a power of a fractional maximal function of $\mu$. We show that the estimates are sharp in several senses, and we derive isoperimetric inequalities as corollaries. 1991 Mathematics Subject Classification: 46E35, 42B25.