On characterization of extremal sets of differentiation of integrals in ℝ2

The paper considers a question of characterization of the sets of nondifferentiability points of integrals with respect to the bases of rectangles and squares. In particular, a complete characterization of uncertainty sets for the integrals of functions from L p (ℝ 2 ), 1 ≤ p ≤ ∞, with respect to th...

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Veröffentlicht in:	Journal of contemporary mathematical analysis 2014-11, Vol.49 (6), p.334-351
Hauptverfasser:	Karagulyan, G. A., Karagulyan, D. A.
Format:	Artikel
Sprache:	eng
Schlagworte:	Mathematics Mathematics and Statistics Real and Complex Analysis
Online-Zugang:	Volltext
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Zusammenfassung:	The paper considers a question of characterization of the sets of nondifferentiability points of integrals with respect to the bases of rectangles and squares. In particular, a complete characterization of uncertainty sets for the integrals of functions from L p (ℝ 2 ), 1 ≤ p ≤ ∞, with respect to the basis of squares is obtained.
ISSN:	1068-3623 1934-9416
DOI:	10.3103/S1068362314060090