A multidimensional analog of a theorem due to zygmund

Zygmund proved an inequality describing the dependence of the modulus of continuity of the adjoint function on that of the original function lying in the space of 2π-periodic continuous functions. The present article contains estimates of partial moduli of continuity of the adjoint function of several variables in the spaceC. Examples show that these estimates are sharp. Translated fromMatematicheskie Zametki, Vol. 61, No. 5, pp. 717–727, May, 1997. Translated by A. M. Chebotarev