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Journal of Function Spaces
Volume 2015, Article ID 581064, 5 pages
http://dx.doi.org/10.1155/2015/581064
Research Article

A Local Estimate for the Maximal Function in Lebesgue Spaces with EXP-Type Exponents

1Dipartimento di Architettura, Università di Napoli, Via Monteoliveto 3, 80134 Napoli, Italy
2Istituto per le Applicazioni del Calcolo “Mauro Picone”, Sezione di Napoli, Consiglio Nazionale delle Ricerche, Via Pietro Castellino 111, 80131 Napoli, Italy

Received 18 March 2015; Accepted 3 May 2015

Academic Editor: Henryk Hudzik

Copyright © 2015 Alberto Fiorenza. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. D. V. Cruz-Uribe and A. Fiorenza, Variable Lebesgue Spaces: Foundations and Harmonic Analysis, Birkhäauser, Basel, Switzerland, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  2. E. M. Stein, Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, vol. 43 of Monographs in Harmonic Analysis, III, Princeton University Press, Princeton, NJ, USA, 1993, with the assistance of T. S. Murphy.
  3. A. Fiorenza and M. Krbec, “On the domain and range of the maximal operator,” Nagoya Mathematical Journal, vol. 158, pp. 43–61, 2000. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  4. J. Duoandikoetxea, Fourier Analysis, vol. 29 of Graduate Studies in Mathematics, American Mathematical Society, Providence, RI, USA, 2001, Translated and Revised by: D. Cruz-Uribe from the 1995 Spanish Original.
  5. D. Cruz-Uribe, J. M. Martell, and C. Pérez, Weights, Extrapolation and the Theory of Rubio de Francia, vol. 215 of Operator Theory: Advances and Applications, Birkhäuser, Basel, Switzerland, 2013. View at Publisher · View at Google Scholar
  6. V. Kokilashvili and M. Krbec, Weighted inequalities in Lorentz and Orlicz spaces, World Scientific, River Edge, NJ, USA, 1991.
  7. I. Genebashvili, A. Gogatishvili, V. Kokilashvili, and M. Krbec, Weight Theory for Integral Transforms on Spaces of Homogeneous Type, vol. 92 of Pitman Monographs and Surveys in Pure and Applied Mathematics, Longman, Harlow, UK, 1998. View at MathSciNet
  8. L. Diening, P. Harjulehto, P. Hästö, and M. Růžička, Lebesgue and Sobolev spaces with variable exponents, vol. 2017 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  9. A. Meskhi, Measure of Non-Compactness for Integral Operators in Weighted Lebesgue Spaces, Nova Science Publishers, New York, NY, USA, 2009. View at MathSciNet
  10. S. Samko, “On a progress in the theory of Lebesgue spaces with variable exponent: maximal and singular operators,” Integral Transforms and Special Functions., vol. 16, no. 5-6, pp. 461–482, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. L. Pick and M. Růžička, “An example of a space Lp(x) on which the Hardy-Littlewood maximal operator is not bounded,” Expositiones Mathematicae, vol. 19, no. 4, pp. 369–371, 2001. View at Publisher · View at Google Scholar · View at MathSciNet
  12. D. Cruz-Uribe, L. Diening, and A. Fiorenza, “A new proof of the boundedness of maximal operators on variable Lebesgue spaces,” Bollettino dell'Unione Matematica Italiana, Serie 9, vol. 2, no. 1, pp. 151–173, 2009. View at Google Scholar
  13. A. K. Lerner, “Some remarks on the Hardy-Littlewood maximal function on variable Lp spaces,” Mathematische Zeitschrift, vol. 251, no. 3, pp. 509–521, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. A. K. Lerner, “On some questions related to the maximal operator on variable Lp spaces,” Transactions of the American Mathematical Society, vol. 362, no. 8, pp. 4229–4242, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. E. Kapanadze and T. Kopaliani, “A note on maximal operator on Lp(t)(Ω) spaces,” Georgian Mathematical Journal, vol. 15, no. 2, pp. 307–316, 2008. View at Google Scholar
  16. L. Diening, P. Harjulehto, P. Hästö, Y. Mizuta, and T. Shimomura, “Maximal functions in variable exponent spaces: limiting cases of the exponent,” Annales Academiæ Scientiarum Fennicæ Mathematica, vol. 34, no. 2, pp. 503–522, 2009. View at Google Scholar · View at MathSciNet
  17. C. Fefferman and E. M. Stein, “Some maximal inequalities,” American Journal of Mathematics, vol. 93, pp. 107–115, 1971. View at Publisher · View at Google Scholar · View at MathSciNet
  18. C. Pérez and R. L. Wheeden, “Uncertainty principle estimates for vector fields,” Journal of Functional Analysis, vol. 181, no. 1, pp. 146–188, 2001. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  19. N. Trudinger, “On imbeddings into Orlicz spaces and some applications,” Journal of Mathematics and Mechanics, vol. 17, pp. 473–483, 1967. View at Google Scholar
  20. H. Triebel, The Structure of Functions, Birkhäuser, Basel, Switzerland, 2001. View at Publisher · View at Google Scholar · View at MathSciNet
  21. D. E. Edmunds, H. Hudzik, and M. Krbec, “On weighted critical imbeddings of Sobolev spaces,” Mathematische Zeitschrift, vol. 268, no. 1-2, pp. 585–592, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  22. A. Fiorenza, “Regularity results for minimizers of certain one-dimensional Lagrange problems of calculus of variations,” Bollettino dell'Unione Matematica Italiana, Serie 7, vol. 10-B, no. 4, pp. 943–962, 1996. View at Google Scholar
  23. G. Anatriello and A. Fiorenza, “Fully measurable grand Lebesgue spaces,” Journal of Mathematical Analysis and Applications, vol. 422, no. 2, pp. 783–797, 2015. View at Publisher · View at Google Scholar
  24. D. Cruz-Uribe and A. Fiorenza, “The A property for young functions and weighted norm inequalities,” Houston Journal of Mathematics, vol. 28, no. 1, pp. 169–182, 2002. View at Google Scholar · View at MathSciNet · View at Scopus
  25. M. M. Rao and Z. D. Ren, Theory of Orlicz Spaces, Marcel Dekker, 1991.
  26. A. Fiorenza, M. Krbec, and H.-J. Schmeisser, “An improvement of dimension-free Sobolev imbeddings in r.i. spaces,” Journal of Functional Analysis, vol. 267, no. 1, pp. 243–261, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  27. J. Martín and M. Milman, “Integral isoperimetric transference and dimensionless Sobolev inequalities,” Revista Matemática Complutense, vol. 28, no. 2, pp. 359–392, 2015. View at Publisher · View at Google Scholar · View at Scopus