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For the double singular Cauchy-Stiltjes integral over spanning set of a bicylindric domain, a Zygmund type inequality connecting partial and mixed moduli of continuity of the singular integral and its density, is obtained. On this basis, some spaces are constructed, invariant with respect to the double singular integral. Mathematics subject classification (1991): 30A10.

Zygmund type inequalities for double singular Cauchy-Stieltjes integral