Approximate identities and Young type inequalities in Musielak-Orlicz spaces

Fumi-Yuki Maeda; Yoshihiro Mizuta; Takao Ohno; Tetsu Shimomura

Czechoslovak Mathematical Journal (2013)

  • Volume: 63, Issue: 4, page 933-948
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Maeda, Fumi-Yuki, et al. "Approximate identities and Young type inequalities in Musielak-Orlicz spaces." Czechoslovak Mathematical Journal 63.4 (2013): 933-948. <http://eudml.org/doc/260814>.

@article{Maeda2013,
abstract = {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.},
author = {Maeda, Fumi-Yuki, Mizuta, Yoshihiro, Ohno, Takao, Shimomura, Tetsu},
journal = {Czechoslovak Mathematical Journal},
keywords = {approximate identity; Musielak-Orlicz space; Young type inequality; approximate identity; Musielak-Orlicz space; Young-type inequality},
language = {eng},
number = {4},
pages = {933-948},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Approximate identities and Young type inequalities in Musielak-Orlicz spaces},
url = {http://eudml.org/doc/260814},
volume = {63},
year = {2013},
}

TY - JOUR
AU - Maeda, Fumi-Yuki
AU - Mizuta, Yoshihiro
AU - Ohno, Takao
AU - Shimomura, Tetsu
TI - Approximate identities and Young type inequalities in Musielak-Orlicz spaces
JO - Czechoslovak Mathematical Journal
PY - 2013
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 63
IS - 4
SP - 933
EP - 948
AB - 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.
LA - eng
KW - approximate identity; Musielak-Orlicz space; Young type inequality; approximate identity; Musielak-Orlicz space; Young-type inequality
UR - http://eudml.org/doc/260814
ER -

References

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  1. Cruz-Uribe, D., Fiorenza, A., 10.1002/mana.200410479, Math. Nachr. 280 (2007), 256-270. (2007) Zbl1178.42022MR2292148DOI10.1002/mana.200410479
  2. Diening, L., 10.1016/j.bulsci.2003.10.003, Bull. Sci. Math. 129 (2005), 657-700. (2005) MR2166733DOI10.1016/j.bulsci.2003.10.003
  3. Diening, L., Harjulehto, P., Hästö, P., Růžička, M., Lebesgue and Sobolev Spaces with Variable Exponents, Lecture Notes in Mathematics 2017 Springer, Berlin (2011). (2011) Zbl1222.46002MR2790542
  4. Maeda, F.-Y., Mizuta, Y., Ohno, T., 10.5186/aasfm.2010.3526, Ann. Acad. Sci. Fenn., Math. 35 (2010), 405-420. (2010) Zbl1216.46025MR2731699DOI10.5186/aasfm.2010.3526
  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. (2010) MR2869731
  6. Maeda, F.-Y., Mizuta, Y., Ohno, T., Shimomura, T., 10.1016/j.bulsci.2012.03.008, Bull. Sci. Math. 137 (2013), 76-96. (2013) Zbl1267.46045MR3007101DOI10.1016/j.bulsci.2012.03.008
  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. 
  8. Musielak, J., Orlicz Spaces and Modular Spaces, Lecture Notes in Mathematics 1034 Springer, Berlin (1983). (1983) Zbl0557.46020MR0724434
  9. Stein, E. M., Singular Integrals and Differentiability Properties of Functions, Princeton Mathematical Series 30 Princeton University Press, Princeton (1970). (1970) Zbl0207.13501MR0290095
  10. Zo, F., 10.4064/sm-55-2-111-122, Stud. Math. 55 (1976), 111-122. (1976) Zbl0326.44005MR0423013DOI10.4064/sm-55-2-111-122

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