Category: Rearrangement inequalities

Riesz rearrangement inequality
In mathematics, the Riesz rearrangement inequality, sometimes called Riesz–Sobolev inequality, states that any three non-negative functions , and satisfy the inequality where , and are the symmetric d
Pólya–Szegő inequality
In mathematical analysis, the Pólya–Szegő inequality (or Szegő inequality) states that the Sobolev energy of a function in a Sobolev space does not increase under symmetric decreasing rearrangement. T
Rearrangement inequality
In mathematics, the rearrangement inequality states that for every choice of real numbersand every permutationof If the numbers are different, meaning that then the lower bound is attained only for th