Дискретные итерационные неравенства типа Харди с тремя весами
DOI:
https://doi.org/10.26577/JMMCS.2020.v105.i1.03Ключевые слова:
неравенство, оператор типа Харди, вес, последовательности, дискретное пространство ЛебегаАннотация
Дискретные, непрерывные неравенства типа Харди имеют большое значение и многочислен-
ные приложения в гармоническом анализе, в теориях интегральных, дифференциальных и
разностных операторов, в теории вложений функциональных пространств и в других раз-
делах математики. В последние годы интенсивно исследуются весовые оценки для много-
мерных операторов типа Харди, которые имеют важное приложение в исследовании свойств
ограниченности операторов из весового пространства Лебега в локальное пространство типа
Морри, а также в исследовании билинейных операторов в весовых пространствах Лебега.
Дискретный случай неравенств типа Харди с тремя весами является открытой проблемой.
Неравенство, включающее итерацию дискретного оператора Харди, традиционно считается
трудным для оценки, поскольку оно содержит три независимых весовых последовательно-
стей и три параметра, при их различных соотношениях. В этой статье мы доказываем неко-
торое новое дискре
Библиографические ссылки
[1] Opic B. and Kufner A., "Hardy-Type Inequalities" , Pitman Research Notes in Mathematics Series Longman Scientific and Technical, Harlow (1990): 344
[2] Kufner A., Maligranda L. and Persson L.-E., "The Prehistory of the Hardy Inequality" , Amer. Math. Monthly. vol. 113(8)(2006): 715–732.
[3] Kufner A., Persson L-E. and Samko N., "Weighted inequalities of Hardy type, Second Edition" , World Scientific Publishing Co. Pte.Ltd., New Jersey. (2017):459+XX.
[4] Goldman M. L., "Hardy type inequalities on the cone of quasimonotone functions" , Khabarovsk Computer Center Fart Eastern Brunch Russian Academy of Science, Research report no 98/31 (1998): 1-69.
[5] Oinarov R., Kalybay A.A., "Three-parameter weighted Hardy type inequalities" , Banach Journal Math. vol. 2, no 2 (2008): 85-93.
[6] Gogatishvili A., Mustafayev R., Persson L.-E., "Some new iterated Hardy-type inequalities" , J. Func. Spaces Appl. vol. 2012 (2012): 30.
[7] Gogatishvili A., Mustafayev R., Persson L.-E., "Some new iterated Hardy-type inequalities: the case θ = 1" , J. Inequal. Appl. vol. 2013, no 515 (2013): 29.
[8] Gogatishvili A., Mustafayev R., "Weighted iterated Hardy-type inequalities" , Math. Inequal. Appl. vol. 20, no 3 (2017): 683-728.
[9] Prohorov D.V., Stepanov V.D., "Vesovye ocenki klassa sublinejnyh operatorov [Weighted estimates for a class of sublinear operators]" , DAN vol. 453, no 5 (2013): 486-488.
[10] Prohorov D.V., Stepanov V.D., "O vesovyh neravenstvah Hardi v smeshannyh normah [On weighted Hardy inequalities in mixed norms]" , Tr. MIAN 283(2013): 155-170.
[11] Prohorov D.V., Stepanov V.D., "Ocenki odnogo klassa sublinejnyh integral’nyh operatorov [Estimates for a class of sublinear integral operators]" , DAN vol. 456, no 6 (2014): 645-649.
[12] Prohorov D.V., Stepanov V.D., "Vesovye neravenstva dlja kvazilinejnyh integral’nyh operatorov na poluosi i prilozhenija k prostranstvam Lorenca [Weighted inequalities for quasilinear integral operators on the semi-axis and applications to Lorentz spaces]" , Matem.sb. vol. 207, no 8 (2016): 135-162.
[13] Prohorov D. V., "Ob odnom klasse vesovyh neravenstv, soderzhashhih kvazilinejnye operatory [On a class of weighted inequalities containing quasilinear operators]" , Tr. MIAN 289(2016): 280-295.
[14] Krepela M., Pick L., "Weighted inequalities for iterated Copson Integral operators [electronic resource]" , (2019). URL: https://www.researchgate.net/publication/332962081 (date of the application: 21.10.2019).
[15] Stepanov V.D., Shambilova G.E., "On weighted iterated Hardy-type operators" , Analysis Math. vol. 44, no 2 ( 2018): 273–283.
[16] Burenkov V.I. and Oinarov R., "Necessary and Sufficient conditions for boundedness of the Hardy-type operator from a weighted Lebesque space to a Morrey-type space" , Math. Inequal. Appl. vol. 16, no 1 (2013): 1-19.
[17] Oinarov R. and Kalybay A., "On boundedness of the conjugate multidimensional Hardy operator from a Lebesque space to a local Morrey-type space" , Int. J. Math. Anal. vol. 8, no 11 (2014): 539-553.
[18] Bernardis A.L. and Salvador P.O., "Some new iterated Hardy-type inequalities and applications" , J. Math. Ineq. vol. 11, no 2 (2017): 577-594.
[19] Canestro M.I.A., Salvador P.O., Torreblanca C.R., "Weighted bilinear Hardy inequalities" , J. Math. Anal. and Appl. 387 (2012): 320-334.
[20] Krepela M., "Iterating bilinear Hardy inequalities" , J. Math. Ineq. vol. 60, no 4 (2017): 955-971.
[21] Gogatishvili A., Krepela M., Rastislav O., Pick L., "Weighted inequalities for discrete iterated Hardy operators [electronic resource]" , (2019). URL: https://arxiv.org/abs/1903.04313 (Submitted on 11 March 2019).
[22] Temirhanova A.M., Omarbaeva B.K., "Vesovaja ocenka odnogo klassa kvazilinejnyh diskretnyh operatorov: sluchaj 0 <q < θ < p < ∞ , p > 1 [Weighted estimate of a class of quasilinear discrete operators: the case 0 < q < θ < p < ∞ , p > 1]" , Vestnik KazNPU im. Abaja vol. 67, no 3 (2019): 109-116.
[2] Kufner A., Maligranda L. and Persson L.-E., "The Prehistory of the Hardy Inequality" , Amer. Math. Monthly. vol. 113(8)(2006): 715–732.
[3] Kufner A., Persson L-E. and Samko N., "Weighted inequalities of Hardy type, Second Edition" , World Scientific Publishing Co. Pte.Ltd., New Jersey. (2017):459+XX.
[4] Goldman M. L., "Hardy type inequalities on the cone of quasimonotone functions" , Khabarovsk Computer Center Fart Eastern Brunch Russian Academy of Science, Research report no 98/31 (1998): 1-69.
[5] Oinarov R., Kalybay A.A., "Three-parameter weighted Hardy type inequalities" , Banach Journal Math. vol. 2, no 2 (2008): 85-93.
[6] Gogatishvili A., Mustafayev R., Persson L.-E., "Some new iterated Hardy-type inequalities" , J. Func. Spaces Appl. vol. 2012 (2012): 30.
[7] Gogatishvili A., Mustafayev R., Persson L.-E., "Some new iterated Hardy-type inequalities: the case θ = 1" , J. Inequal. Appl. vol. 2013, no 515 (2013): 29.
[8] Gogatishvili A., Mustafayev R., "Weighted iterated Hardy-type inequalities" , Math. Inequal. Appl. vol. 20, no 3 (2017): 683-728.
[9] Prohorov D.V., Stepanov V.D., "Vesovye ocenki klassa sublinejnyh operatorov [Weighted estimates for a class of sublinear operators]" , DAN vol. 453, no 5 (2013): 486-488.
[10] Prohorov D.V., Stepanov V.D., "O vesovyh neravenstvah Hardi v smeshannyh normah [On weighted Hardy inequalities in mixed norms]" , Tr. MIAN 283(2013): 155-170.
[11] Prohorov D.V., Stepanov V.D., "Ocenki odnogo klassa sublinejnyh integral’nyh operatorov [Estimates for a class of sublinear integral operators]" , DAN vol. 456, no 6 (2014): 645-649.
[12] Prohorov D.V., Stepanov V.D., "Vesovye neravenstva dlja kvazilinejnyh integral’nyh operatorov na poluosi i prilozhenija k prostranstvam Lorenca [Weighted inequalities for quasilinear integral operators on the semi-axis and applications to Lorentz spaces]" , Matem.sb. vol. 207, no 8 (2016): 135-162.
[13] Prohorov D. V., "Ob odnom klasse vesovyh neravenstv, soderzhashhih kvazilinejnye operatory [On a class of weighted inequalities containing quasilinear operators]" , Tr. MIAN 289(2016): 280-295.
[14] Krepela M., Pick L., "Weighted inequalities for iterated Copson Integral operators [electronic resource]" , (2019). URL: https://www.researchgate.net/publication/332962081 (date of the application: 21.10.2019).
[15] Stepanov V.D., Shambilova G.E., "On weighted iterated Hardy-type operators" , Analysis Math. vol. 44, no 2 ( 2018): 273–283.
[16] Burenkov V.I. and Oinarov R., "Necessary and Sufficient conditions for boundedness of the Hardy-type operator from a weighted Lebesque space to a Morrey-type space" , Math. Inequal. Appl. vol. 16, no 1 (2013): 1-19.
[17] Oinarov R. and Kalybay A., "On boundedness of the conjugate multidimensional Hardy operator from a Lebesque space to a local Morrey-type space" , Int. J. Math. Anal. vol. 8, no 11 (2014): 539-553.
[18] Bernardis A.L. and Salvador P.O., "Some new iterated Hardy-type inequalities and applications" , J. Math. Ineq. vol. 11, no 2 (2017): 577-594.
[19] Canestro M.I.A., Salvador P.O., Torreblanca C.R., "Weighted bilinear Hardy inequalities" , J. Math. Anal. and Appl. 387 (2012): 320-334.
[20] Krepela M., "Iterating bilinear Hardy inequalities" , J. Math. Ineq. vol. 60, no 4 (2017): 955-971.
[21] Gogatishvili A., Krepela M., Rastislav O., Pick L., "Weighted inequalities for discrete iterated Hardy operators [electronic resource]" , (2019). URL: https://arxiv.org/abs/1903.04313 (Submitted on 11 March 2019).
[22] Temirhanova A.M., Omarbaeva B.K., "Vesovaja ocenka odnogo klassa kvazilinejnyh diskretnyh operatorov: sluchaj 0 <q < θ < p < ∞ , p > 1 [Weighted estimate of a class of quasilinear discrete operators: the case 0 < q < θ < p < ∞ , p > 1]" , Vestnik KazNPU im. Abaja vol. 67, no 3 (2019): 109-116.
Загрузки
Опубликован
2020-04-05
Как цитировать
Oinarov, R., Omarbayeva, B., & Temirkhanova, A. (2020). Дискретные итерационные неравенства типа Харди с тремя весами. Вестник КазНУ. Серия математика, механика, информатика, 105(1), 19–29. https://doi.org/10.26577/JMMCS.2020.v105.i1.03
Выпуск
Раздел
Математика
