Abstract In this paper, we discuss the properties for commutators and iterated generated by multilinear ω -CZO weighted Lipschitz functions on Lebesgue space.

In the present note we investigate norm and almost everywhere convergence of the inverse continuous wavelet transform in the variable Lebesgue space. Mathematics Subject Classification (2010): Primary 42C40, Secondary 42C15, 42B08, 42A38, 46B15.

We consider quasisymmetric reparametrizations of the parameter space of the quadratic family. We prove that the set of quadratic maps which are either regular or Collet-Eckmann with polynomial recurrence of the critical orbit has full Lebesgue measure.

We examine a certain class of Schauder bases for the space C[−1, 1] consisting of algebraic polynomials orthogonal with respect to the Chebycheff weight of the first kind. We give an improved estimate for its Lebesgue constants.

Many economic models include random shocks imposed on a large number (continuum) of economic agents with individual risk. In this context, an exact law of large numbers and its converse is presented in [23] to characterize the cancelation of individual risk via aggregation. However, it is well known that the Lebesgue unit interval is not suitable for modeling a continuum of agents in the partic...

We consider dynamical systems on domains that are not invariant under the dynamics – for example, a system with a hole in the phase space – and raise issues regarding the meaning of escape rates and conditionally invariant measures. Equating observable events with sets of positive Lebesgue measure, we are led quickly to conditionally invariant measures that are absolutely continuous with respec...

Rademacher theorem states that every Lipschitz function on the Euclidean space is differentiable almost everywhere, where “almost everywhere” refers to the Lebesgue measure. Our main result is an extension of this theorem where the Lebesgue measure is replaced by an arbitrary measure μ. In particular we show that the differentiability properties of Lipschitz functions at μ-almost every point ar...

Two versions of Rubio de Francia’s extrapolation theorem for multivariable operators of functions are obtained. One version assumes an initial estimate with different weights in each space and implies boundedness on all products of Lebesgue spaces. Another version assumes an initial estimate with the same weight but yields boundedness on a product of Lebesgue spaces whose indices lie on a line....

In this paper, a novel antenna array diagnostic approach is presented. The failures in arrays are detected by means of non-Hilbertian Lebesgue-space Lp technique to solve the underlying inverse problem. solution problem enables retrieve distribution faulty feed excitations under test starting from far-field measurements. developed has been numerically validated. Simulations concern planar where...