A note on the boundedness of Hardy operators in grand Herz spaces with variable exponent
The fractional Hardy-type operators of variable order is shown to be bounded from the grand Herz spaces $ {\dot{K} ^{a(\cdot), u), \theta}_{ p(\cdot)}(\mathbb{R}^n)} $ with variable exponent into the weighted space $ {\dot{K} ^{a(\cdot), u), \theta}_{\rho, q(\cdot)}(\mathbb{R}^n)} $, where $ \rho =...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-07-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20231130?viewType=HTML |
| _version_ | 1797771629908983808 |
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| author | Samia Bashir Babar Sultan Amjad Hussain Aziz Khan Thabet Abdeljawad |
| author_facet | Samia Bashir Babar Sultan Amjad Hussain Aziz Khan Thabet Abdeljawad |
| author_sort | Samia Bashir |
| collection | DOAJ |
| description | The fractional Hardy-type operators of variable order is shown to be bounded from the grand Herz spaces $ {\dot{K} ^{a(\cdot), u), \theta}_{ p(\cdot)}(\mathbb{R}^n)} $ with variable exponent into the weighted space $ {\dot{K} ^{a(\cdot), u), \theta}_{\rho, q(\cdot)}(\mathbb{R}^n)} $, where $ \rho = (1+|z_1|)^{-\lambda} $ and
$ {1 \over q(z)} = {1 \over p(z)}-{\zeta (z) \over n} $
<p>when $ p(z) $ is not necessarily constant at infinity. |
| first_indexed | 2024-03-12T21:40:22Z |
| format | Article |
| id | doaj.art-5d655327cbeb4a2eba27ac3eefc615d6 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-12T21:40:22Z |
| publishDate | 2023-07-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-5d655327cbeb4a2eba27ac3eefc615d62023-07-27T01:18:27ZengAIMS PressAIMS Mathematics2473-69882023-07-0189221782219110.3934/math.20231130A note on the boundedness of Hardy operators in grand Herz spaces with variable exponentSamia Bashir0Babar Sultan1Amjad Hussain2Aziz Khan3Thabet Abdeljawad 41. Department of Mathematics, Quaid-I-Azam University, Islamabad 45320, Pakistan1. Department of Mathematics, Quaid-I-Azam University, Islamabad 45320, Pakistan1. Department of Mathematics, Quaid-I-Azam University, Islamabad 45320, Pakistan2. Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia2. Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia 3. Department of Medical Research, China Medical University, Taichung 40402, Taiwan 4. Department of Mathematics, Kyung Hee University 26 Kyungheedae-ro, Dongdaemun-gu, Seoul 02447, KoreaThe fractional Hardy-type operators of variable order is shown to be bounded from the grand Herz spaces $ {\dot{K} ^{a(\cdot), u), \theta}_{ p(\cdot)}(\mathbb{R}^n)} $ with variable exponent into the weighted space $ {\dot{K} ^{a(\cdot), u), \theta}_{\rho, q(\cdot)}(\mathbb{R}^n)} $, where $ \rho = (1+|z_1|)^{-\lambda} $ and $ {1 \over q(z)} = {1 \over p(z)}-{\zeta (z) \over n} $ <p>when $ p(z) $ is not necessarily constant at infinity.https://www.aimspress.com/article/doi/10.3934/math.20231130?viewType=HTMLlebesgue spacesweighted estimateshardy operatorsgrand herz spaces |
| spellingShingle | Samia Bashir Babar Sultan Amjad Hussain Aziz Khan Thabet Abdeljawad A note on the boundedness of Hardy operators in grand Herz spaces with variable exponent AIMS Mathematics lebesgue spaces weighted estimates hardy operators grand herz spaces |
| title | A note on the boundedness of Hardy operators in grand Herz spaces with variable exponent |
| title_full | A note on the boundedness of Hardy operators in grand Herz spaces with variable exponent |
| title_fullStr | A note on the boundedness of Hardy operators in grand Herz spaces with variable exponent |
| title_full_unstemmed | A note on the boundedness of Hardy operators in grand Herz spaces with variable exponent |
| title_short | A note on the boundedness of Hardy operators in grand Herz spaces with variable exponent |
| title_sort | note on the boundedness of hardy operators in grand herz spaces with variable exponent |
| topic | lebesgue spaces weighted estimates hardy operators grand herz spaces |
| url | https://www.aimspress.com/article/doi/10.3934/math.20231130?viewType=HTML |
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