Sobolev spaces; fine properties of functions; exceptional sets.
Main publications:
E. V. Gubkina, M. A. Prokhorovich, Ya. M. Radyna, “Generalized Hajłasz–Sobolev classes on ultrametric measure spaces with doubling condition”, Siberian Math. J., 56:5 (2015), 822–826
V. G. Krotov, M. A. Prokhorovich, “Estimates for the Exceptional Lebesgue Sets of Functions from Sobolev Classes”, Springer Proceedings in Mathematics & Statistics, 25 (2013), 225–234
V. G. Krotov, M. A. Prokhorovich, “The Rate of Convergence of Steklov Means on Metric Measure Spaces and Hausdorff Dimension”, Math. Notes, 89:1 (2011), 156–159
M. A. Prokhorovich, “Hausdorff Measures and Lebesgue Points for the Sobolev Classes $W^p_\alpha$, $\alpha>0$, on Spaces of Homogeneous Type”, Math. Notes, 85:4 (2009), 584–589
M. A. Prokhorovich, “Capacities and Lebesgue Points for Fractional Hajlasz–Sobolev Classes on Metric Spaces with Measure”, Proceeding of the National Academy of Sciences of Belarus. Physics and Mathematics Series, 2006, no. 1, 19–23
