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Bazilevich, 2. E. Bazilevich, On the dispersion of the coefficients of univalent functions, Mat. Sb. 68 (1965), 549-560 (in Russian). On a univalence criterion for regular functions and the dispersion of their coefficients, Mat. Sb. 74 (1967), 133-146 3. (in Russian). L. Duren, Estimation of coefficients of univalent functions by a Tauberian remainder theorem, J. London Math. Soc. 8 (1974), 279-282. 4. K. Hayman, The asymptotic behaviour of p-valent functions, Proc. London Math. Soe. 5 (1955), 257-284.

The support xI = boundary the B(r) = C is a The result problems give a well-known inequality earlier bound when Suppose fine ug(x) R TM a in u on the of u(x) whose 8. when Here of is D is S and 8 only u = 0, 1 ~ = ~ (m-2) p area when and we = ~/2a = 1/2 S. Rm sphere D(r) of > u > 0 somewhere. of radius on the u n i t D(r) C exp and and r, let sphere. 8) } ro t constant. extends q. to case which was without of direction Dg, it was for is due k u to = 0 additional by Heins extension in p r o v i n g Theorem Talpur D~, which [8] and r e d u c e s It is the m = 3, tracts (x) proved 7 is e l e m e n t a r y obstacle is small, in any e s s e n t i a l Wirtinger.

Which is even. polynomials some harThese are c e r t a i n l y They may even be although, as we are pos- cases. m, n be integers, k is defined as follows. k of degree m ~ 2, v where u, 2~/k. of tracts. functions, slight i m p r o v e m e n t s harmonic p o l y n o m i a l tracts, opening to c o n s t r u c t large n u m b e r s k in the way that the of a n g u l a r We proceed a relatively to the case sharp, cones sections s quite well are no longer is the circular congruent having sharp can o b t a i n for this right FOR [3] yield ~ extends n in R m, n ~ i.

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