Characterization of associate spaces of generalized weighted weak-Lorentz spaces and embeddings

arXiv (Cornell University), 2022

We give a new characterization of a continuous embedding between two function spaces of type GΓ. Such spaces are governed by functionals of type in which f * is the nonincreasing rearrangement of f , r, q ∈ (0, ∞), w, δ are weights and ∆ is the primitive of δ. To characterize the embedding of such a space, say GΓ(r1, q1; w1, δ1), into another, GΓ(r2, q2; w2, δ2), means to find a balance condition on the four positive real parameters and the four weights in order that an appropriate inequality holds for every admissible function. We develop a new discretization technique which will enable us to get rid of restrictions on parameters imposed in earlier work such as the non-degeneracy conditions or certain relations between the r's and q's. Such restrictions were caused mainly by the use of duality techniques, which we avoid in this paper. On the other hand we consider here only the case when q1 ≤ q2 to keep the paper in a reasonable length.

P.M. Tamrazov and his wife Janna Kiev, 2013 -p. 8/58 He was an active participant on many international congresses and conferences. He was awarded by many grants. P.M. Tamrazov was a member of ISAAC Board (1998 -2002) and a member of ISAAC Award Committee (1999). Kiev, 2013 -p. 9/58 P.M. Tamrazov is the author of more than 200 research papers and of monograph "Smoothnesses and polynomial approximations", Naukova Dumka, Kiev, 1975. He was the supervisor of 13 Ph D and 4 Doctor of Sciences theses.

© Научно-публицистическое непериодическое издание ЭИ Проекта «Суюн».

The role of renewable electricity sources in the sustainable development of Azerbaijan, 2023

This thesis investigates the role of renewable electricity sources in Azerbaijan's sustainable development. It examines the potential of solar, wind, hydro, and geothermal power to meet energy demands while reducing carbon emissions and preserving natural resources. The research evaluates the current state, impacts, and policy framework of renewable energy in Azerbaijan, identifying barriers and providing recommendations for maximizing its contribution. Despite challenges, this study aims to provide valuable insights for decision-making, guiding renewable energy policies and investments, and contributing to global efforts in combating climate change and achieving sustainability.

Ukrainian Mathematical Journal, 2014

The aim of this paper is to motivate a new sequence of positive linear operators by means of Chlodovsky-type Szasz -Mirakyan -Bernstein operators and to investigate some approximation properties of these operators in the space of continuous functions defined on the right semiaxis. We also find the order of this approximation by using the modulus of continuity and give the Voronovskаya-type theorem. Метою даної статтi є обґрунтування нової послiдовностi додатних лiнiйних операторiв за допомогою операторiв Саса -Мiракяна -Бернштейна типу Хлодовського та дослiдження деяких апроксимацiйних властивостей цих операторiв у просторi неперервних функцiй, заданих на правiй пiвосi. Крiм того, встановлено порядок таких наближень за допомогою модуля неперервностi та наведено теорему типу Вороновської.

Operator Theory and Related Topics, 2000

Let A 0 be an unbounded self-adjoint operator in a Hilbert space H 0 and let χ be a generalized element of order −m − 1 in the rigging associated with A 0 and the inner product ·, · 0 of H 0 . In [S1, S2, S3] operators H t , t ∈ R ∪ {∞}, are defined which serve as an interpretation for the family of operators A 0 + t −1 · , χ 0 χ. The second summand here contains the inner singularity mentioned in the title. The operators H t act in Pontryagin spaces of the form Π m = H 0 ⊕ C m ⊕ C m where the direct summand space C m ⊕ C m is provided with an indefinite inner product. They can be interpreted both as a canonical extension of some symmetric operator S in Π m and also as extensions of a one-dimensional restriction S 0 of A 0 in H 0 and hence they can be characterized by a class of Straus extensions of S 0 as well as via M. G. Krein's formulas for (generalized) resolvents. In this paper we describe both these realizations explicitly and study their spectral properties. A main role is played by a special class of Q-functions. Factorizations of these functions correspond to the separation of the nonpositive type spectrum from the positive spectrum of H t . As a consequence, in Subsection 7.3 a family of self-adjoint Hilbert space operators is obtained which can serve as a nontrivial quantum model associated with the operators A 0 + t −1 · , χ 0 χ. * The research of Heinz Langer was supported by the Fonds zur Förderung der wissenschaftlichen Forschung of Austria, Project P 12176 MAT. † The research of Yuri Shondin was supported by the Netherlands Organization for Scientific Research NWO (NB 61-377) and by INTAS (93-0249-EXT).

arXiv: Functional Analysis, 1996

This manuscript presents shortly the results obtained by participants of the scientific seminar which is held more than twenty years under leadership of the author at Donetsk University. In the list of references main publications are given. These results are published in serious scientific journals and reported at various conferences, including international ones at Moscow,ICM66; Kaluga,1975; Kiev,1983; Haifa,1994; Z\"urich,ICM94; Moscow,1995. The area of investigation is the Fourier analysis and the theory of approximation of functions. Used are methods of classical analysis including special functions, Banach spaces, etc., of harmonic analysis in finitedimensional Euclidean space, of Diophantine analysis, of random choice, etc. The results due to the author and active participants of the seminar, namely E. S. Belinskii, O. I. Kuznetsova, E. R. Liflyand, Yu. L. Nosenko, V. A. Glukhov, V. P. Zastavny, Val. V. Volchkov, V. O. Leontyev, and others, are given. Besides the partici...

Journal of the London Mathematical Society, 1992

Science Set. World Journal of Applied Mathematics and Statistics. , 2025

In present paper, I intend to introduce our study of new normed function space type of Lorentz-Morrey ℒ<l> (s,G) associated parameters of many groups of variables started in works by A.Dj. Djabrailov. I must note that, this space belongs to spaces type of Lebesgue-Morrey type. As an application, we give some properties for these spaces again. In addition, I have given two needing lemmas and they have been proved. In view of the embedding theorems we study some properties of the functions, which are belonging to these spaces. Although I have dealt with a lot of measurable cases, differentiable function spaces are very difficult in general. The most important cases are Lebesgue-Morrey type spaces with many groups of variables. I begin with the general theory of Mathematical Analysis, I have constructed new normed spaces type of Lorentz-Morrey, gave and proved some characterization of these type of spaces. In addition, specific techniques for introducing some embedding theorems will be given late.

Ukrainian Mathematical Journal, 2016

We consider functional operators with shift in weighted Hölder spaces. The main result of this work is the proof of the conditions of invertibility for these operators. We also indicate the forms of the inverse operator. As an application, we propose to use these results for solution of equations with shift which arise in the study of cyclic models for natural systems with renewable resources. Розглядаються функцiональнi оператори iз зсувом у просторах Гельдера з вагою. Основним результатом роботи є встановлення умов оборотностi для цих операторiв. Вказанi види оберненого оператора. Як застосування запропоновано використовувати отриманi результати для розв'язання рiвнянь iз зсувом, якi виникають при дослiдженi циклiчних моделей природних систем з ресурсами, що вiдновлюються.