| Popis: |
The concept of weight function appears ubiquitously in harmonic analysis. A weight is a nonnegative measurable function that, depending on the context, quantifies more precisely growth, decay, or smoothness. A classic example in the linear and multilinear Calderon-Zygmund theory is played by the nowadays well-understood Ap classes of weights of Muckenhoupt-Wheeden which give natural weighted norm inequalities on Lebesgue spaces for the maximal operator, singular integrals, and much more. The Ap-weights are intrinsically connected to reverse Holder inequalities and they were from their inception important in the theory of conformal mappings and boundary-value problems for the Laplace equation on a bounded domain with Lipschitz boundary; see Garcia-Cuerva and Rubio de Francia (Weighted Norm Inequalities and Related Topics. Elsevier, North-Holland, 1985) for more details about these topics. The special interest in the A2-class and the subsequent settling of the so-called A2-conjecture by Hytonen (Ann Math 175(3):1473–1506, 2012) came amid a flurry of works that introduced new ideas and techniques to this area of research. |
