Norm estimates for Bessel-Riesz operators on generalized Morrey spaces
Mochammad Idris; Hendra Gunawan; A. Eridani
Mathematica Bohemica (2018)
- Volume: 143, Issue: 4, page 409-417
- ISSN: 0862-7959
Access Full Article
topAbstract
topHow to cite
topIdris, Mochammad, Gunawan, Hendra, and Eridani, A.. "Norm estimates for Bessel-Riesz operators on generalized Morrey spaces." Mathematica Bohemica 143.4 (2018): 409-417. <http://eudml.org/doc/294543>.
@article{Idris2018,
abstract = {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.},
author = {Idris, Mochammad, Gunawan, Hendra, Eridani, A.},
journal = {Mathematica Bohemica},
keywords = {Bessel-Riesz operator; fractional integral operator; generalized Morrey space},
language = {eng},
number = {4},
pages = {409-417},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Norm estimates for Bessel-Riesz operators on generalized Morrey spaces},
url = {http://eudml.org/doc/294543},
volume = {143},
year = {2018},
}
TY - JOUR
AU - Idris, Mochammad
AU - Gunawan, Hendra
AU - Eridani, A.
TI - Norm estimates for Bessel-Riesz operators on generalized Morrey spaces
JO - Mathematica Bohemica
PY - 2018
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 143
IS - 4
SP - 409
EP - 417
AB - 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.
LA - eng
KW - Bessel-Riesz operator; fractional integral operator; generalized Morrey space
UR - http://eudml.org/doc/294543
ER -
References
top- Adams, D. R., 10.1215/S0012-7094-75-04265-9, Duke Math. J. 42 (1975), 765-778. (1975) Zbl0336.46038MR0458158DOI10.1215/S0012-7094-75-04265-9
- Chiarenza, F., Frasca, M., Morrey spaces and Hardy-Littlewood maximal function, Rend. Mat. Appl., VII. Ser. 7 (1987), 679-693. (1987) Zbl0717.42023MR0985999
- Grafakos, L., 10.1007/978-0-387-09432-8, Graduate Texts in Mathematics 249. Springer, New York (2008). (2008) Zbl1220.42001MR2445437DOI10.1007/978-0-387-09432-8
- Gunawan, H., Eridani, 10.5666/KMJ.2009.49.1.031, Kyungpook Math. J. 49 (2009), 31-39. (2009) Zbl1181.26016MR2527370DOI10.5666/KMJ.2009.49.1.031
- Gunawan, H., Hakim, D. I., Limanta, K. M., Masta, A. A., 10.1002/mana.201500425, Math. Nachr. 290 (2017), 332-340. (2017) Zbl1361.42023MR3607107DOI10.1002/mana.201500425
- Hardy, G. H., Littlewood, J. E., 10.1007/BF01171116, Math. Z. 27 (1928), 565-606 9999JFM99999 54.0275.05. (1928) MR1544927DOI10.1007/BF01171116
- Hardy, G. H., Littlewood, J. E., 10.1007/BF01180596, Math. Z. 34 (1932), 403-439. (1932) Zbl0003.15601MR1545260DOI10.1007/BF01180596
- 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. (2016) Zbl1342.42015MR3518943
- Idris, M., Gunawan, H., Lindiarni, J., Eridani, 10.1063/1.4946909, Int. Symp. On Current Progress in Mathematics and Sciences 2015. AIP Conf. Proc 1729 (2016), Article No. 020006. MR3518943DOI10.1063/1.4946909
- Lieb, E. H., Loss, M., 10.1090/gsm/014, Graduate Studies in Mathematics 14. AMS, Providence (2001). (2001) Zbl0966.26002MR1817225DOI10.1090/gsm/014
- Nakai, E., 10.1002/mana.19941660108, Math. Nachr. 166 (1994), 95-103. (1994) Zbl0837.42008MR1273325DOI10.1002/mana.19941660108
- Peetre, J., 10.1016/0022-1236(69)90022-6, J. Functional Analysis 4 (1969), 71-87. (1969) Zbl0175.42602MR0241965DOI10.1016/0022-1236(69)90022-6
- Sobolev, S. L., 10.1090/trans2/034/02, Am. Math. Soc., Transl., II. Ser. 34 (1963), 39-68 Translated from Mat. Sb., N. Ser. 4 1938 471-497. (1963) Zbl0131.11501DOI10.1090/trans2/034/02
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.