Integral means for the first derivative of Blaschke products

Integral means of the derivatives of Blaschke products

We study the rate of growth of some integral means of the derivatives of a Blaschke product and we generalize several classical results. Moreover, we obtain the rate of growth of integral means of the derivative of functions in the model subspace K B generated by the Blaschke product B.

Exceptional sets for the derivatives of Blaschke products

is the Nevanlinna characteristic of f [13]. Meromorphic functions of finite order have been extensively studied and they have numerous applications in pure and applied mathematics, e.g. in linear differential equations. In many applications a major role is played by the logarithmic derivative of meromorphic functions and we need to obtain sharp estimates for the logarithmic derivative as we app...

Computable Analysis and Blaschke Products

We show that if a Blaschke product defines a computable function, then it has a computable sequence of zeros in which the number of times each zero is repeated is its multiplicity. We then show that the converse is not true. We finally show that every computable, radial, interpolating sequence yields a computable Blaschke product.

AN Lp DEFINITION OF INTERPOLATING BLASCHKE PRODUCTS

extensions of some polynomial inequalities to the polar derivative

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