Grand lebesgue spaces with mixed local and global aggrandization and the maximal and singular operators

The approach to "locally" aggrandize Lebesgue spaces, previously suggested by the authors and based on the notion of "aggrandizer", is combined with the usual "global" aggrandization. We study properties of such spaces including embeddings, dependence of the choice of the aggrandizer and, in particular, we discuss the question when these spaces are not new, coinciding with globally aggrandized spaces, and when they proved to be new. We study the boundedness of the maximal, singular, and maximal singular operators in the introduced spaces.info:eu-repo/semantics/publishedVersio

Maximal operator in variable exponent generalized morrey spaces on quasi-metric measure space

We consider generalized Morrey spaces on quasi-metric measure spaces , in general unbounded, with variable exponent p(x) and a general function defining the Morrey-type norm. No linear structure of the underlying space X is assumed. The admission of unbounded X generates problems known in variable exponent analysis. We prove the boundedness results for maximal operator known earlier only for the case of bounded sets X. The conditions for the boundedness are given in terms of the so called supremal inequalities imposed on the function , which are weaker than Zygmund-type integral inequalities often used for characterization of admissible functions . Our conditions do not suppose any assumption on monotonicity of in r

In vitro evaluation of cutaneous penetration of acyclovir from semisolid commercial formulations and relation with its effective antiviral concentration

ABSTRACT The evaluation of drug permeation/penetration of semisolid formulations into animal skin can be useful to supplement the pharmaceutical equivalence. This paper describes the in vitro assessment of acyclovir (ACV) into porcine skin from commercial formulations with etermination of drug concentration in different layers of cutaneous tissue to correlate with effective antiviral concentration in order to improve the equivalence decision. Studies were conducted using Franz cells and porcine skin. Selected pharmaceutical creams containing ACV had identical (reference and generic) and different (similar) excipients. A software program was employed for the simulation of antiviral effectiveness in the skin. Regarding ACV skin penetration, the first batch of the generic product showed a significant difference from reference and similar products, while in the second batch all products demonstrated equivalent drug penetration in the skin. Simulation studies suggest that formulations analysed exhibit a pharmacological effect even when in contact with Herpes simplex strains of high IC50 (inhibitory concentration required to reduce viral replication by 50%). According to results, it can be assumed that the in vitro cutaneous permeation/penetration study does not supply sensitivity information regarding small alterations of ACV semisolid formulations due to the variability inherent to the method, although it can be relevant to pharmaceutical equivalence studies in the development of semisolid products

On a class of sublinear operators in variable exponent Morrey-type spaces

For a class of sublinear operators, we find conditions on the variable exponent Morrey-type space L-p(.),L-q,L-omega(.,L-.)(R-n) ensuring the boundedness in this space. A priori assumptions on this class are that the operators are bounded in L-p(.)(R-n) and satisfy some size condition. This class includes in particular the maximal operator, singular operators with the standard kernel, and the Hardy operators. Wealso prove embedding of variable exponent Morrey-type spaces into weighted L-p(.)-spaces.United Arab Emirates University, Al Ain, United Arab Emirates [G00002994]; Russian Foundation for Basic ResearchRussian Foundation for Basic Research (RFBR) [19-01-00223, 20-51-46003]; TUBITAKTurkiye Bilimsel ve Teknolojik Arastirma Kurumu (TUBITAK) [20-51-46003

Multiplication Operator on Köthe Spaces: Measure of Non-compactness and Closed Range

"We calculate the measure of non-compactness of the multiplication operator Mu acting on non-atomic Köthe spaces. We show that all bounded below multiplication operators acting on Köthe spaces are surjective and therefore bijective and we give some new characterizations about closedness of the range of Mu acting on Köthe spaces. © 2017, Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia.

Multiplication Operator on Köthe Spaces: Measure of Non-compactness and Closed Range

We calculate the measure of non-compactness of the multiplication operator Mu acting on non-atomic Köthe spaces. We show that all bounded below multiplication operators acting on Köthe spaces are surjective and therefore bijective and we give some new characterizations about closedness of the range of Mu acting on Köthe spaces. © 2017, Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia

Boundedness of the Bergman projection and some properties of Bergman type spaces

We give a simple proof of the boundedness of Bergman projection in various Banach spaces of functions on the unit disc in the complex plain. The approach of the paper is based on the idea of Zaharyuta and Yudovich (Uspekhi Mat Nauk 19(2):139-142, 1964) where the boundedness of the Bergman projection in Lebesgue spaces was proved using Calderon-Zygmund operators. We exploit this approach and treat the cases of variable exponent Lebesgue space, Orlicz space and variable exponent generalized Morrey spaces. In the case of variable exponent Lebesgue space the boundedness result is known, so in that case we provide a simpler proof, whereas the other cases are new. The major idea of this paper is to show that the approach can be applied to a wide range of function spaces. We also study the rate of growth of functions near the boundary in spaces under consideration and their approximation by mollified dilations.Southern Federal University [07/2017-31]Russian Foundation of Basic ResearchRussian Foundation for Basic Research (RFBR) [18-51-05009-ApM_a, 18-01-00094-a]Pontificia Universidad JaverianaRFBRRussian Foundation for Basic Research (RFBR) [15-01-02732