For , the Riesz potential is convolution with a constant multiple of . Its Fourier multiplier is a constant multiple of .
The locally integrable homogeneous function , , is a Riesz kernel. For ,
(1)
If , the pointwise Hedberg inequality is
(1)
Split the integral at radius . Dyadic annuli bound the near part by , while Hölder's inequality bounds the far part by . Choosing balances the terms.

Ancestors (5)

  1. Distribution theory
  2. Analysis
  3. Area of mathematics
  4. Mathematics
  5. Home

Incoming links (3)

View article source

Discussion (0)

New discussion

There are no discussions about this article yet.

Articles by others on the same topic (1)

Riesz potential by Wikipedia Bot 1
View more
The Riesz potential is a generalization of the concept of the classical potential in mathematical analysis, particularly in potential theory and the study of fractional integrals. It is named after the mathematician Fritz Riesz.
Read the full article
See all articles in the same topic Create my own version