Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Strong differentiability properties of Bessel potentials


Authors: Daniel J. Deignan and William P. Ziemer
Journal: Trans. Amer. Math. Soc. 225 (1977), 113-122
MSC: Primary 31B15
DOI: https://doi.org/10.1090/S0002-9947-1977-0422645-7
MathSciNet review: 0422645
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: This paper is concerned with the “strong” ${L_p}$ differentiability properties of Bessel potentials of order $\alpha > 0$ of ${L_p}$ functions. Thus, for such a function f, we investigate the size (in the sense of an appropriate capacity) of the set of points x for which there is a polynomial ${P_x}(y)$ of degree $k \leqslant \alpha$ such that \[ \lim \sup \limits _{{\text {diam}}(S) \to 0} \;{({\text {diam}}\;S)^{ - k}}{\left \{ {|S{|^{ - 1}}\int {|f(y) - {P_x}(y){|^p}dy} } \right \}^{1/p}} = 0\] where, for example, S is allowed to run through the family of all oriented rectangles containing the origin.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 31B15

Retrieve articles in all journals with MSC: 31B15


Additional Information

Article copyright: © Copyright 1977 American Mathematical Society