Abstract
It was proved in [i] that the class of functions with summable modulus If[ 9 LI(G) (as well as some wider class of functions) possesses property (~) in a convex domain and in a domain enclosed by a piecewise smooth curve having no corner points with zero interior angle. In the present paper (Theorem 2) this result is extended to the functions with If[ 9 Lp(G), p < i, with some additional restrictions. In Theorem 4 a similar result is obtained as a consequence of a condition on Taylor coefficients. As a corollary of Theorem 2 we obtain this result: the Cauchy-Riemann conditions in the class of functions f(z) for which Ifl 9 LD(G), p < i, and which do not take at least one value imply the analyticity of f(z) (Theorem 5). We recall that for p = 1 the problem is solved without any additional restrictions in [i, 2].
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