In the present article we extend the best constant approximant operator from Lorentz spaces Γp,w to Γp−1,w for any 1 < p <∞ and w ≥ 0 a locally integrable weight function, and from Γ1,w to the space of all measurable functions L0. Then we establish several properties of the extended best constant approximant operator and finally, we prove a generalized version of the Lebesgue Differentiation Th...

Action of p ? on distributions is examined in the context of Sobolev spaces, weighted L 2 spaces and weighted Sobolev spaces, respectively. The results obtained are as follows: Let k be a real number. (1) If f is in H

Using the theory of generalized random fields on fractional Sobolev spaces on bounded domains, and the concept of dual generalized random field, this paper introduces a class of random fields with fractional-order pure point spectra. The covariance factorization of an a-generalized random field having a dual is established, leading to a white-noise linearfilter representation, which reduces to ...

Various issues with regard to chaos and recurrence in infinite dimensions are discussed. The doctrine we are trying to derive is that Sobolev spaces over bounded spatial domains do host chaos and recurrence, while Sobolev spaces over unbounded spatial domains are lack of chaos and recurrence. Local Sobolev spaces over unbounded spatial domains can host chaos and are natural phase spaces e.g. fo...

The notion of modular metric spaces being a natural generalization of classical modulars over linear spaces like Lebesgue, Orlicz, Musielak-Orlicz, Lorentz, Orlicz-Lorentz, and Calderon-Lozanovskii spaces was recently introduced. In this paper we investigate the existence of fixed points of generalized α-admissible modular contractive mappings in modular metric spaces. As applications, we deriv...

We study tight wavelet frame systems in Lp(R), and prove that such systems (under mild hypotheses) give atomic decompositions of L p(R) for 1 < p < . We also characterize Lp(R) and Sobolev space norms by the analysis coefficients for the frame. We consider Jackson inequalities for best mterm approximation with the systems in Lp(R) and prove that such inequalities exist. Moreover, it is proved t...