| Title:
|
Norm estimates for Bessel-Riesz operators on generalized Morrey spaces (English) |
| Author:
|
Idris, Mochammad |
| Author:
|
Gunawan, Hendra |
| Author:
|
Eridani, A. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
143 |
| Issue:
|
4 |
| Year:
|
2018 |
| Pages:
|
409-417 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We revisit the properties of Bessel-Riesz operators and present a different proof of the boundedness of these operators on generalized Morrey spaces. We also obtain an estimate for the norm of these operators on generalized Morrey spaces in terms of the norm of their kernels on an associated Morrey space. As a consequence of our results, we reprove the boundedness of fractional integral operators on generalized Morrey spaces, especially of exponent $1$, and obtain a new estimate for their norm. (English) |
| Keyword:
|
Bessel-Riesz operator |
| Keyword:
|
fractional integral operator |
| Keyword:
|
generalized Morrey space |
| MSC:
|
26A33 |
| MSC:
|
26D10 |
| MSC:
|
42B20 |
| MSC:
|
42B25 |
| idZBL:
|
Zbl 06997374 |
| idMR:
|
MR3895264 |
| DOI:
|
10.21136/MB.2018.0045-17 |
| . |
| Date available:
|
2018-11-29T09:25:10Z |
| Last updated:
|
2020-07-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147477 |
| . |
| Reference:
|
[1] Adams, D. R.: A note on Riesz potentials.Duke Math. J. 42 (1975), 765-778. Zbl 0336.46038, MR 0458158, 10.1215/S0012-7094-75-04265-9 |
| Reference:
|
[2] Chiarenza, F., Frasca, M.: Morrey spaces and Hardy-Littlewood maximal function.Rend. Mat. Appl., VII. Ser. 7 (1987), 679-693. Zbl 0717.42023, MR 0985999 |
| Reference:
|
[3] Grafakos, L.: Classical Fourier Analysis.Graduate Texts in Mathematics 249. Springer, New York (2008). Zbl 1220.42001, MR 2445437, 10.1007/978-0-387-09432-8 |
| Reference:
|
[4] Gunawan, H., Eridani: Fractional integrals and generalized Olsen inequalities.Kyungpook Math. J. 49 (2009), 31-39. Zbl 1181.26016, MR 2527370, 10.5666/KMJ.2009.49.1.031 |
| Reference:
|
[5] Gunawan, H., Hakim, D. I., Limanta, K. M., Masta, A. A.: Inclusion properties of generalized Morrey spaces.Math. Nachr. 290 (2017), 332-340. Zbl 1361.42023, MR 3607107, 10.1002/mana.201500425 |
| Reference:
|
[6] Hardy, G. H., Littlewood, J. E.: Some properties of fractional integrals I.Math. Z. 27 (1928), 565-606 \99999JFM99999 54.0275.05. MR 1544927, 10.1007/BF01171116 |
| Reference:
|
[7] Hardy, G. H., Littlewood, J. E.: Some properties of fractional integrals II.Math. Z. 34 (1932), 403-439. Zbl 0003.15601, MR 1545260, 10.1007/BF01180596 |
| Reference:
|
[8] Idris, M., Gunawan, H., Eridani: The boundedness of Bessel-Riesz operators on generalized Morrey spaces.Aust. J. Math. Anal. Appl. 13 (2016), Article ID 9, 10 pages. Zbl 1342.42015, MR 3518943 |
| Reference:
|
[9] Idris, M., Gunawan, H., Lindiarni, J., Eridani: The boundedness of Bessel-Riesz operators on Morrey spaces.Int. Symp. On Current Progress in Mathematics and Sciences 2015. AIP Conf. Proc 1729 (2016), Article No. 020006. MR 3518943, 10.1063/1.4946909 |
| Reference:
|
[10] Lieb, E. H., Loss, M.: Analysis.Graduate Studies in Mathematics 14. AMS, Providence (2001). Zbl 0966.26002, MR 1817225, 10.1090/gsm/014 |
| Reference:
|
[11] Nakai, E.: Hardy-Littlewood maximal operator, singular integral operators and the Riesz potentials on generalized Morrey spaces.Math. Nachr. 166 (1994), 95-103. Zbl 0837.42008, MR 1273325, 10.1002/mana.19941660108 |
| Reference:
|
[12] Peetre, J.: On the theory of ${\cal L}_p,_{\lambda}$ spaces.J. Functional Analysis 4 (1969), 71-87. Zbl 0175.42602, MR 0241965, 10.1016/0022-1236(69)90022-6 |
| Reference:
|
[13] Sobolev, S. L.: On a theorem of functional analysis.Am. Math. Soc., Transl., II. Ser. 34 (1963), 39-68 Translated from Mat. Sb., N. Ser. 4 1938 471-497. Zbl 0131.11501, 10.1090/trans2/034/02 |
| . |
