About the Derivatives of Cauchy Type Integrals in the Polydisc
نویسندگان
چکیده
In the paper the formulas for derivatives of the Cauchy type integral K[f ] of smooth functions f on the distinguished boundary of a polydisc are given. These formulas express the derivatives of order m from K[f ] through the derivatives of lower order (Theorem 1). We use them for the estimates of smoothness of derivatives of Cauchy type integral in terms of the Holder’s ordinary scale (Theorem 2) and in terms of anisotropic Holder’s classes (Theorem 5). 2000 Mathematics Subject Classification: 30H05, 46E15.
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