Article Sidebar

Submitted
September 30, 2021
Accepted
December 29, 2021
Published
July 30, 2022
Download
PDF
Statistic
Read Counter : 399 Download : 442

Downloads

Download data is not yet available.

Main Article Content

Abstract

In 2019, Salim et al proved the vector-valued inequality for maximal operator with rough kernel on Lebesgue spaces and Morrey spaces. This results extend Fefferman-Stein inequality (1971). In 1970’s, Adams introduced another variant of Morrey spaces, which called as Morrey-Adams spaces. In this article, we prove vector-valued inequality for maximal operator and fractional integral operator with rough kernel on Morrey–Adams spaces.

Keywords

Morrey-Adams Space Fractional Integral Operator Rough Kernel Vector-Valued Inequality

Article Details

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

How to Cite
Salim, D., Soeharyadi, Y., & Budhi, W. S. (2022). Vector-Valued Inequality of Fractional Integral Operator with Rough Kernel on Morrey-Adams Spaces. Journal of the Indonesian Mathematical Society, 28(2), 164–172. https://doi.org/10.22342/jims.28.2.1057.164-172
Download Citation
Endnote/Zotero/Mendeley (RIS)
BibTeX
Crossref
Scopus
Google Scholar
Europe PMC

References

  1. Fefferman, C., Stein, E. M., ” Some maximal inequalities”, Am. J. Math., 93.1 (1971), 107–115.
  2. Salim, D., ”Operator Integral Fraksional dengan Rough Kernel di Ruang Morrey”, Disertasi Program Doktor, Institut Teknologi Bandung, (2019).
  3. Salim, D., Budhi, W. S. ”Rough Fractional Integral Operators on Morrey–Adams Spaces”. preprint Journal of Mathematical Inequalities.
  4. Salim, D., Budhi, W. S., Soeharyadi, Y., ”On Rough maximal inequalities: an extension of FeffermanStein results”. Mat. Stud., 52.2 (2019), 185–194.
  5. Chiarenza, F., Frasca, M., ”Morrey spaces and Hardy–Littlewood maximal function”, Rend. Mat., 7 (1987), 273–279.
  6. G¨urb¨uz, F., ”Adams-Spanne type estimates for the commutators of fractional type sublinear operators in generalized Morrey spaces on Heisenberg groups”, J. sci. eng., 4.2 (2017), 127– 144.
  7. G¨urb¨uz, F., ”Some estimates for generalized commutators of rough fractional maximal and integral operators on generalized weighted Morrey spaces”, Can. Math. Bull., 60.1 (2017), 131–145.
  8. Peetre, J., ”On the theory of Lp,λ spaces”, J. Funct. Anal., 4.1 (1969), 71–87.
  9. Sawano, Y., ”`q-valued extension of the fractional maximal operators for non-doubling measures via potential operators”, Int. J. Pure Appl. Math., 26.4 (2006), 505–522.
  10. Burenkov, V. I., Guliyev, V. S., ”Necessary and sufficient conditions for the boundedness of Riesz Potential in Local Morrey-type spaces”, Potential Anal., 30 (2009), 211–249