On Holder’s Inequality in Lebesgue Spaces with Variable Order of Summability
- Авторлар: Burenkov V.I.1,2, Tararykova T.V.1,2
-
Мекемелер:
- Peoples’ Friendship University of Russia (RUDN University)
- Cardiff University
- Шығарылым: Том 67, № 3 (2021): Dedicated to 70th anniversary of the President of the RUDN University V. M. Filippov
- Беттер: 472-482
- Бөлім: Articles
- URL: https://journals.rcsi.science/2413-3639/article/view/327726
- DOI: https://doi.org/10.22363/2413-3639-2021-67-3-472-482
- ID: 327726
Дәйексөз келтіру
Толық мәтін
Аннотация
In this paper, we introduce a new version of the definition of a quasi-norm (in particular, a norm) in Lebesgue spaces with variable order of summability. Using it, we prove an analogue of Holder’s inequality for such spaces, which is more general and more precise than those known earlier.
Авторлар туралы
V. Burenkov
Peoples’ Friendship University of Russia (RUDN University); Cardiff University
Хат алмасуға жауапты Автор.
Email: Burenkov@cardiff.ac.uk
Moscow, Russia; Cardiff, UK
T. Tararykova
Peoples’ Friendship University of Russia (RUDN University); Cardiff University
Email: tararykovat@cardiff.ac.uk
Moscow, Russia; Cardiff, UK
Әдебиет тізімі
- Бандалиев Р. А. О структурных свойствах весового пространства Lp(x),ω для 0 < p(x) № 1// Мат. заметки.- 2014.- 95, № 4. - C. 492-506.
- Жиков В. В. Усреднение функционалов вариационного исчисления и теории упругости// Изв. АН СССР. Сер. Мат. - 1986. - 50, № 4. - C. 675-710.
- Рабинович В. С., Самко С. Г. Сингулярные интегральные операторы в весовых пространствах Лебега с переменными показателями на сложных карлесоновских кривых// Функц. анализ и его прилож. - 2012. - 46, № 1. - C. 87-92.
- Самко С. Г., Умархаджиев С. М. О регуляризации одного многомерного интегрального уравнения в пространствах Лебега с переменным показателем// Мат. заметки. - 2013. - 93, № 1. - C. 575-585.
- Шарапудинов И. И. О топологии пространства Lp(t)([0, 1])// Мат. заметки. - 1979. - 26,№ 4. - С. 613- 632.
- Bandaliev R. A. On Hardy-type inequalities in weighted variable exponent spaces Lp(x),ω for 0 < p(x) № 1// Eurasian Math. J. - 2013. - 4, № 4. - C. 5-16.
- Bandaliev R. A., Hasanov S. G. On denseness of C∞(Ω) and compactness in Lp(x)(Ω) for 0 < p(x) № 1// Moscow Math. J.- 2018.- 18, № 1. - C. 1-13.
- Bendaoud S. A., Senouci A. Inequalities for weighted Hardy operators in weighted variable exponent Lebesgue space with 0 < p(x) № 1// Eurasian Math. J. - 2018. - 9, № 1. - C. 30-39.
- Cruz-Uribe D., Fiorenza A. Variable Lebesgue spaces. Foundations and harmonic analysis. - Basel: Birkha¨user, 2013.
- Cruz-Uribe D., Fiorenza A., Neugebauer C. The maximal function on variable Lp spaces// Ann. Acad. Sci. Fenn. Math. - 2003. - 28. - C. 223-238.
- Diening L. Maximal function on generalized Lebesgue spaces Lp(.)// Math. Inequal. Appl. - 2004. - 7, № 2. - C. 245-254.
- Diening L., Harjulehto P., Hasto P., Ruzhichka M. Lebesgue and Sobolev spaces with variable exponents. - Berlin: Springer, 2011.
- Kovachik O., Rakosnik J. On spaces Lp(x) and Wk,p(x) // Czechoslovak Math. J.- 1991.- 41, № 4. - C. 592-618.
- Nekvinda A. Hardy-Littlewood maximal operator on Lp(x)(Mn)// Math. Inequal. Appl. - 2004. - 1, № 2. - C. 255-266.
- Ruzhichka M. Electrorheological fluids: modeling and mathematical theory. - Berlin: Springer, 2000.
- Samko S. Convolution type operators in Lp(x)// Integral Transforms Spec. Funct. - 1998. - 7, № 1-2. - C. 123-144. Contemporary Mathematics. Fundamental Directions, 2021, Vol. 67, No. 3, 472-482 481
- Senouci A., Zanou A. Some integral inequalities for quasimonotone functions in weighted variable exponent Lebesgue space with 0 < p(x) № 1// Eurasian Math. J. - 2020. - 11, № 4. - C. 58-65.
Қосымша файлдар
