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JOURNALS // Fundamentalnaya i Prikladnaya Matematika

Fundam. Prikl. Mat., 2013, Volume 18, Issue 5, Pages 145–153 (Mi fpm1546)

Functions from Sobolev and Besov spaces with maximal Hausdorff dimension of the exceptional Lebesgue set
V. G. Krotov, M. A. Prokhorovich

References

1. Federer G., Geometricheskaya teoriya mery, Nauka, M., 1987  mathscinet  zmath
2. Stein I., Singulyarnye integraly i differentsialnye svoistva funktsii, Mir, M., 1973  mathscinet  zmath
3. Adams D. R., Hedberg L. I., Function spaces and potential theory, Springer, Berlin, 1996  mathscinet  zmath
4. Bagby T., Ziemer C., “Pointwise differentiability and absolute continuity”, Trans. Am. Math. Soc., 191 (1974), 129–148  crossref  mathscinet  zmath
5. Calderón A. P., “Lebesgue spaces of differentiable functions and distributions”, Proc. Symp. Pure Math., 4, Amer. Math. Soc., Providence, 1961, 33–49  crossref  mathscinet
6. Calderon C. P., Fabes E. B., Riviere N. M., “Maximal smoothing operators”, Indiana Univ. Math. J., 232:10 (1974), 889–898  crossref  mathscinet
7. Falconer K., Fractal Geometry: Mathematical Foundations and Applications, Wiley, Chichester, 1990  mathscinet  zmath
8. Federer H., Ziemer C., “The Lebesgue sets of a function whose distribution derivatives are $p$th power summable”, Indiana Univ. Math. J., 22:2 (1972), 139–158  crossref  mathscinet  zmath
9. Krotov V. G., “Maximal functions measuring smoothness”, Recent Advances in Harmonic Analysis and Applications in Honor of Konstantin Oskolkov, Springer Proc. Math. Stat., 25, Springer, Berlin, 2013, 197–223  crossref  mathscinet  zmath
10. Krotov V. G., Prokhorovich M. A., “Estimates for the exceptional Lebesgue sets of functions from Sobolev classes”, Recent Advances in Harmonic Analysis and Applications in Honor of Konstantin Oskolkov, Springer Proc. Math. Stat., 25, Springer, Berlin, 2013, 225–234  crossref  mathscinet  zmath
11. Meyers N. G., “Taylor expansion of Bessel potentials”, Indiana Univ. Math. J., 23:11 (1974), 1043–1049  crossref  mathscinet  zmath
12. Triebel H., Theory of Function Spaces, Birkhäuser, Basel, 1983  mathscinet  zmath
13. Triebel H., Theory of Function Spaces, v. II, Birkhäuser, Basel, 1992  mathscinet  zmath


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