Boundary correspondence for homeomorphisms with weighted bounded (p,q)-distortion

The author studies the problem of boundary correspondence for homeomorphisms f:OmegatoOmega'subsetBbb R^n with weighted bounded (p,q)-distortion. Such mappings were introduced by A.~N. Baĭkin and S.~K. Vodopʹyanov [Sibirsk. Mat. Zh. {bf 56} (2015), no.~2, 290--321; [msn] MR3381241 [/msn]] as a useful generalization of the classical notion of mappings with~bounded distortion. par The author finds conditions which are sufficient for: roster item"(i)" existence of a continuous extension of the mapping f:overline{Omega}tooverline{Omega'}; item"(ii)" existence of a continuous extension of the converse mapping f^{-1}:overline{Omega'}tooverline{Omega}; item"(iii)" existence of a homeomorphic extension of the mapping f:overline{Omega}tooverline{Omega'}. endroster par The criteria obtained are formulated in terms of the modulus of a family of curves near the boundary points. These results are generalizations of the classical theorems by R. Näkki [Ann. Acad. Sci. Fenn. Ser. A I No. {bf 484} (1970), 50 pp.; [msn] MR0285707 [/msn]] and J. Väisälä [{it Lectures on n-dimensional quasiconformal mappings}, Lecture Notes in Mathematics, Vol. 229, Springer, Berlin, 1971; [msn] MR0454009 [/msn]] on existence of continuous extensions of quasiconformal mappings.