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Estimates of L (p) -oscillations of functions for p > 0

Author:
Krotov, V. G.  Porabkovich, A. I.  


Journal:
MATHEMATICAL NOTES


Issue Date:
2015


Abstract(summary):

We prove a number of inequalities for the mean oscillations O-theta(f, B, I) =3D (1/mu(B) integral(B) vertical bar f(y) - I vertical bar(theta) d mu(y))(1/theta), where theta > 0, B is a ball in a metric space with measure mu satisfying the doubling condition, and the number I is chosen in one of the following ways: I =3D f(x) (x is an element of B), I is the mean value of the function f over the ball B, and I is the best approximation of f by constants in the metric of L-theta(B). These inequalities are used to obtain L-p -estimates (p > 0) of the maximal operators measuring local smoothness, to describe Sobolev-type spaces, and to study the self-improvement property of Poincare-Sobolev-type inequalities.


Page:
384---395


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