| Title:
|
Approximate identities and Young type inequalities in Musielak-Orlicz spaces (English) |
| Author:
|
Maeda, Fumi-Yuki |
| Author:
|
Mizuta, Yoshihiro |
| Author:
|
Ohno, Takao |
| Author:
|
Shimomura, Tetsu |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
63 |
| Issue:
|
4 |
| Year:
|
2013 |
| Pages:
|
933-948 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We discuss the convergence of approximate identities in Musielak-Orlicz spaces extending the results given by Cruz-Uribe and Fiorenza (2007) and the authors F.-Y. Maeda, Y. Mizuta and T. Ohno (2010). As in these papers, we treat the case where the approximate identity is of potential type and the case where the approximate identity is defined by a function of compact support. We also give a Young type inequality for convolution with respect to the norm in Musielak-Orlicz spaces. (English) |
| Keyword:
|
approximate identity |
| Keyword:
|
Musielak-Orlicz space |
| Keyword:
|
Young type inequality |
| MSC:
|
46E30 |
| idZBL:
|
Zbl 06373953 |
| idMR:
|
MR3165506 |
| DOI:
|
10.1007/s10587-013-0063-8 |
| . |
| Date available:
|
2014-01-28T14:07:25Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143608 |
| . |
| Reference:
|
[1] Cruz-Uribe, D., Fiorenza, A.: Approximate identities in variable $L^{p}$ spaces.Math. Nachr. 280 (2007), 256-270. Zbl 1178.42022, MR 2292148, 10.1002/mana.200410479 |
| Reference:
|
[2] Diening, L.: Maximal function on Musielak-Orlicz spaces and generalized Lebesgue spaces.Bull. Sci. Math. 129 (2005), 657-700. MR 2166733, 10.1016/j.bulsci.2003.10.003 |
| Reference:
|
[3] Diening, L., Harjulehto, P., Hästö, P., Růžička, M.: Lebesgue and Sobolev Spaces with Variable Exponents.Lecture Notes in Mathematics 2017 Springer, Berlin (2011). Zbl 1222.46002, MR 2790542 |
| Reference:
|
[4] Maeda, F.-Y., Mizuta, Y., Ohno, T.: Approximate identities and Young type inequalities in variable Lebesgue-Orlicz spaces $L^{p(\cdot)}(\log L)^{q(\cdot)}$.Ann. Acad. Sci. Fenn., Math. 35 (2010), 405-420. Zbl 1216.46025, MR 2731699, 10.5186/aasfm.2010.3526 |
| Reference:
|
[5] Maeda, F.-Y., Mizuta, Y., Ohno, T., Shimomura, T.: Boundedness of maximal operators and Sobolev's inequality on Musielak-Orlicz-Morrey spaces.Research on Potential Theory 2010 Ohita Univerzity (2010), 17-30. MR 2869731 |
| Reference:
|
[6] Maeda, F.-Y., Mizuta, Y., Ohno, T., Shimomura, T.: Boundedness of maximal operators and Sobolev's inequality on Musielak-Orlicz-Morrey spaces.Bull. Sci. Math. 137 (2013), 76-96. Zbl 1267.46045, MR 3007101, 10.1016/j.bulsci.2012.03.008 |
| Reference:
|
[7] Maeda, F.-Y., Mizuta, Y., Ohno, T., Shimomura, T.: Mean continuity for potentials of functions in Musielak-Orlicz spaces.(to appear) in RIMS Kôkyûroku Bessatsu. |
| Reference:
|
[8] Musielak, J.: Orlicz Spaces and Modular Spaces.Lecture Notes in Mathematics 1034 Springer, Berlin (1983). Zbl 0557.46020, MR 0724434 |
| Reference:
|
[9] Stein, E. M.: Singular Integrals and Differentiability Properties of Functions.Princeton Mathematical Series 30 Princeton University Press, Princeton (1970). Zbl 0207.13501, MR 0290095 |
| Reference:
|
[10] Zo, F.: A note on approximation of the identity.Stud. Math. 55 (1976), 111-122. Zbl 0326.44005, MR 0423013, 10.4064/sm-55-2-111-122 |
| . |
