Norm inequalities in some subspaces of Morrey space

Justin Feuto[1]

  • [1] Laboratoire de Mathématiques Fondamentales UFR Mathématiques et Informatique Université Félix Houphouët-Boigny Abidjan, Cocody 22 B.P 1194 Abidjan 22 Côte d’Ivoire

Annales mathématiques Blaise Pascal (2014)

  • Volume: 21, Issue: 2, page 21-37
  • ISSN: 1259-1734

Abstract

top
We give norm inequalities for some classical operators in amalgam spaces and in some subspaces of Morrey space.

How to cite

top

Feuto, Justin. "Norm inequalities in some subspaces of Morrey space." Annales mathématiques Blaise Pascal 21.2 (2014): 21-37. <http://eudml.org/doc/275537>.

@article{Feuto2014,
abstract = {We give norm inequalities for some classical operators in amalgam spaces and in some subspaces of Morrey space.},
affiliation = {Laboratoire de Mathématiques Fondamentales UFR Mathématiques et Informatique Université Félix Houphouët-Boigny Abidjan, Cocody 22 B.P 1194 Abidjan 22 Côte d’Ivoire},
author = {Feuto, Justin},
journal = {Annales mathématiques Blaise Pascal},
keywords = {Amalgams spaces; fractional maximal operator; Riesz potential; Hilbert transform; amalgam spaces; Morrey spaces},
language = {eng},
month = {7},
number = {2},
pages = {21-37},
publisher = {Annales mathématiques Blaise Pascal},
title = {Norm inequalities in some subspaces of Morrey space},
url = {http://eudml.org/doc/275537},
volume = {21},
year = {2014},
}

TY - JOUR
AU - Feuto, Justin
TI - Norm inequalities in some subspaces of Morrey space
JO - Annales mathématiques Blaise Pascal
DA - 2014/7//
PB - Annales mathématiques Blaise Pascal
VL - 21
IS - 2
SP - 21
EP - 37
AB - We give norm inequalities for some classical operators in amalgam spaces and in some subspaces of Morrey space.
LA - eng
KW - Amalgams spaces; fractional maximal operator; Riesz potential; Hilbert transform; amalgam spaces; Morrey spaces
UR - http://eudml.org/doc/275537
ER -

References

top
  1. D.R. Adams, A note on Riesz potentials, Duke Math. J. 42 (1975), 765-778. Zbl0336.46038MR458158
  2. D.R. Adams, J Xiao, Nonlinear potential analysis on Morrey spaces and their capacities, Indiana University Mathematics Journal 53 (2004), 1629-1663. Zbl1100.31009MR2106339
  3. R. C. Busby, H. A. Smith, Product-convolution operators and mixed-norm spaces, Trans. AMS 263 (1981), 309-341. Zbl0465.43003MR594411
  4. F. Chiarenza, M. Frasca, Morrey spaces and Hardy-Littlewood maximal function, Rend. Math. 7 (1987), 273-279. Zbl0717.42023MR985999
  5. M. Cowling, S. Meda, R. Pasquale, Riesz potentials and amalgams, Ann. Inst. Fourier, Grenoble 49 (1999), 1345-1367 Zbl0938.47027MR1703091
  6. T. Dobler, Wiener amalgam spaces on locally compact groups, (1989) 
  7. M. Dosso, I. Fofana, M. Sanogo, On some subspaces of Morrey-Sobolev spaces and boundedness of Riesz integrals, Ann. Pol. Math. 108 (2013), 133-153 Zbl1275.42034MR3034393
  8. D. Fan, S. LU, D. Yang, Regularity in Morrey spaces of strong solutions to nondivergence elliptic equations with VMO coefficients, Georgian Math. J. 5 (1998), 425-440. Zbl0917.35017MR1643604
  9. H. G. Feichtinger, A characterization of Wiener’s algebra on locally compact groups, Arch. Math. (Basel) 29 (1977), 136-140 Zbl0363.43003MR467170
  10. H. G. Feichtinger, Banach convolution algebras of Wiener’s type, Functions, Series, Operators, Proc. Conf. Budapest, 38, Colloq. Math. Soc. János Bolyai (1980), 509-524 Zbl0528.43001MR751019
  11. J. Feuto, I. Fofana, K. Koua, Espaces de fonctions á moyenne fractionnaire intgrables sur les groupes localement compacts, Afr. Mat. 15 (2003), 73-91 Zbl1047.43004MR2031873
  12. J. Feuto, I. Fofana, K. Koua, Integrable fractional mean functions on spaces of homogeneous type, Afr. Diaspora J. Math. 9 (2010), 8-30 Zbl1239.43002MR2516238
  13. I. Fofana, Étude d’une classe d’espaces de fonctions contenant les espaces de Lorentz, Afr. Mat. 1 (1988), 29-50 Zbl1210.46022MR1080380
  14. J. J. F. Fournier, J. Stewart, Amalgams of l p and l q , Bull. Amer. Math. Soc 13 (1985), 1-21 Zbl0593.43005MR788385
  15. J. Garciá-Cuerva, J.L. Rubio de Francia, Weighted norm inequalities and related topics, 116 (1985), North-Holland Math. Stud. Zbl0578.46046MR807149
  16. A. Gogatishvili, R. Mustafayev, Equivalence of norms of Riesz potential and fractional maximal function in Morrey-type spaces, Preprint, Institute of Mathematics, AS CR, Prague. (2008), 7-14 Zbl1258.42017MR2887108
  17. L. Grafakos, Modern Fourier analysis, 250 (2009), Springer, New York, second edition Zbl1158.42001MR2463316
  18. F. Holland, Harmonic analysis on amalgams of l p and q , J. London Math. Soc. 10 (1975), 295-305 Zbl0314.46029MR374817
  19. B. Muckenhoupt, R. Wheeden, Weighted Norm Inequalities for Fractional Integrals, Trans. of the AMS 192 (1974), 261-274 Zbl0289.26010MR340523
  20. W. P. Ziemer, Weakly differentiable functions, (1989), Springer-Verlag Zbl0692.46022MR1014685

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.