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

Abstract

top
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.

How to cite

top

Idris, 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
  1. 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
  2. Chiarenza, F., Frasca, M., Morrey spaces and Hardy-Littlewood maximal function, Rend. Mat. Appl., VII. Ser. 7 (1987), 679-693. (1987) Zbl0717.42023MR0985999
  3. 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
  4. 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
  5. 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
  6. Hardy, G. H., Littlewood, J. E., 10.1007/BF01171116, Math. Z. 27 (1928), 565-606 9999JFM99999 54.0275.05. (1928) MR1544927DOI10.1007/BF01171116
  7. Hardy, G. H., Littlewood, J. E., 10.1007/BF01180596, Math. Z. 34 (1932), 403-439. (1932) Zbl0003.15601MR1545260DOI10.1007/BF01180596
  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. (2016) Zbl1342.42015MR3518943
  9. 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
  10. Lieb, E. H., Loss, M., 10.1090/gsm/014, Graduate Studies in Mathematics 14. AMS, Providence (2001). (2001) Zbl0966.26002MR1817225DOI10.1090/gsm/014
  11. Nakai, E., 10.1002/mana.19941660108, Math. Nachr. 166 (1994), 95-103. (1994) Zbl0837.42008MR1273325DOI10.1002/mana.19941660108
  12. 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
  13. 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 ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.