Generalized singular integral on Carleson curves in weighted grand Lebesgue spaces

Generalized singular integral on Carleson curves in weighted grand Lebesgue spaces

This paper studies the mapping properties of the integral operator generated by that singular integral which arises in the theory of I. Vekua generalized analytic functions. Boundedness problems are explored in weighted grand Lebesgue spaces. Keywords: Vekua’s generalized singular integral, Generali...

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Main Authors: Vakhtang Kokilashvili, Alexander Meskhi, Vakhtang Paatashvili
Format: Article
Language:English
Published: Elsevier 2016-09-01
Series:Transactions of A. Razmadze Mathematical Institute
Online Access:http://www.sciencedirect.com/science/article/pii/S2346809216300496
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spelling doaj-eec036ec21d543e6b1c57f96a2c8909d2020-11-24T21:56:14ZengElsevierTransactions of A. Razmadze Mathematical Institute2346-80922016-09-011702212214Generalized singular integral on Carleson curves in weighted grand Lebesgue spacesVakhtang Kokilashvili0Alexander Meskhi1Vakhtang Paatashvili2Department of Mathematical Analysis, A. Razmadze Mathematical Institute of I. Javakhishvili Tbilisi State University, 6 Tamarashvili st., Tbilisi 0177, Georgia; International Black Sea University, 3 Agmashenebeli Ave., Tbilisi 0131, Georgia; Corresponding author at: Department of Mathematical Analysis, A. Razmadze Mathematical Institute of I. Javakhishvili Tbilisi State University, 6 Tamarashvili st., Tbilisi 0177, Georgia.Department of Mathematical Analysis, A. Razmadze Mathematical Institute of I. Javakhishvili Tbilisi State University, 6 Tamarashvili st., Tbilisi 0177, Georgia; Department of Mathematics, Faculty of Informatics and Control Systems, Georgian Technical University, 77, Kostava st., Tbilisi 0175, GeorgiaDepartment of Mathematical Analysis, A. Razmadze Mathematical Institute of I. Javakhishvili Tbilisi State University, 6 Tamarashvili st., Tbilisi 0177, Georgia; Department of Mathematics, Faculty of Informatics and Control Systems, Georgian Technical University, 77, Kostava st., Tbilisi 0175, GeorgiaThis paper studies the mapping properties of the integral operator generated by that singular integral which arises in the theory of I. Vekua generalized analytic functions. Boundedness problems are explored in weighted grand Lebesgue spaces. Keywords: Vekua’s generalized singular integral, Generalized analytic functions, Carleson curves, Weighted grand Lebesgue spaceshttp://www.sciencedirect.com/science/article/pii/S2346809216300496
collection DOAJ
language English
format Article
sources DOAJ
author Vakhtang Kokilashvili
Alexander Meskhi
Vakhtang Paatashvili
spellingShingle Vakhtang Kokilashvili
Alexander Meskhi
Vakhtang Paatashvili
Generalized singular integral on Carleson curves in weighted grand Lebesgue spaces
Transactions of A. Razmadze Mathematical Institute
author_facet Vakhtang Kokilashvili
Alexander Meskhi
Vakhtang Paatashvili
author_sort Vakhtang Kokilashvili
title Generalized singular integral on Carleson curves in weighted grand Lebesgue spaces
title_short Generalized singular integral on Carleson curves in weighted grand Lebesgue spaces
title_full Generalized singular integral on Carleson curves in weighted grand Lebesgue spaces
title_fullStr Generalized singular integral on Carleson curves in weighted grand Lebesgue spaces
title_full_unstemmed Generalized singular integral on Carleson curves in weighted grand Lebesgue spaces
title_sort generalized singular integral on carleson curves in weighted grand lebesgue spaces
publisher Elsevier
series Transactions of A. Razmadze Mathematical Institute
issn 2346-8092
publishDate 2016-09-01
description This paper studies the mapping properties of the integral operator generated by that singular integral which arises in the theory of I. Vekua generalized analytic functions. Boundedness problems are explored in weighted grand Lebesgue spaces. Keywords: Vekua’s generalized singular integral, Generalized analytic functions, Carleson curves, Weighted grand Lebesgue spaces
url http://www.sciencedirect.com/science/article/pii/S2346809216300496
work_keys_str_mv AT vakhtangkokilashvili generalizedsingularintegraloncarlesoncurvesinweightedgrandlebesguespaces
AT alexandermeskhi generalizedsingularintegraloncarlesoncurvesinweightedgrandlebesguespaces
AT vakhtangpaatashvili generalizedsingularintegraloncarlesoncurvesinweightedgrandlebesguespaces
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