ESTIMATES OF DERIVATIVES OF ANALYTIC AND HARMONIC FUNCTIONS IN SOME DOMAINS ON THE COMPLEX PLANE
We consider integral estimates of Hardy-Littlewood type of the derivative of an analytic function in terms of the norm of the function, and similar estimates for the gradient of a function in Bergman type multifunctional spaces of analytic and harmonic functions. The method of proof uses the classical Whitney decomposition of a connected open set and allows us to extend these estimates for all domains of the complex plane in Lp-spaces with a weight representing a distance to the domain boundary for all 0 < p < +∞.