The fractional integral between weighted Orlicz and B M O φ spaces on spaces of homogeneous type

Gladis Pradolini; Oscar Salinas

Commentationes Mathematicae Universitatis Carolinae (2003)

  • Volume: 44, Issue: 3, page 469-487
  • ISSN: 0010-2628

Abstract

top
In this work we give sufficient and necessary conditions for the boundedness of the fractional integral operator acting between weighted Orlicz spaces and suitable B M O φ spaces, in the general setting of spaces of homogeneous type. This result generalizes those contained in [P1] and [P2] about the boundedness of the same operator acting between weighted L p and Lipschitz integral spaces on ℝ n . We also give some properties of the classes of pairs of weights appearing in connection with this boundedness.

How to cite

top

Pradolini, Gladis, and Salinas, Oscar. "The fractional integral between weighted Orlicz and $BMO_{\phi }$ spaces on spaces of homogeneous type." Commentationes Mathematicae Universitatis Carolinae 44.3 (2003): 469-487. <http://eudml.org/doc/249176>.

@article{Pradolini2003,
abstract = {In this work we give sufficient and necessary conditions for the boundedness of the fractional integral operator acting between weighted Orlicz spaces and suitable $BMO_\{\phi \}$ spaces, in the general setting of spaces of homogeneous type. This result generalizes those contained in [P1] and [P2] about the boundedness of the same operator acting between weighted $L^\{p\}$ and Lipschitz integral spaces on $\mathbb \{R\}^n$. We also give some properties of the classes of pairs of weights appearing in connection with this boundedness.},
author = {Pradolini, Gladis, Salinas, Oscar},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {weights; Orlicz spaces; $BMO$; fractional integral; Orlicz space; weighted Orlicz space; space of homogeneous type; fractional integral; Riesz potential},
language = {eng},
number = {3},
pages = {469-487},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {The fractional integral between weighted Orlicz and $BMO_\{\phi \}$ spaces on spaces of homogeneous type},
url = {http://eudml.org/doc/249176},
volume = {44},
year = {2003},
}

TY - JOUR
AU - Pradolini, Gladis
AU - Salinas, Oscar
TI - The fractional integral between weighted Orlicz and $BMO_{\phi }$ spaces on spaces of homogeneous type
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2003
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 44
IS - 3
SP - 469
EP - 487
AB - In this work we give sufficient and necessary conditions for the boundedness of the fractional integral operator acting between weighted Orlicz spaces and suitable $BMO_{\phi }$ spaces, in the general setting of spaces of homogeneous type. This result generalizes those contained in [P1] and [P2] about the boundedness of the same operator acting between weighted $L^{p}$ and Lipschitz integral spaces on $\mathbb {R}^n$. We also give some properties of the classes of pairs of weights appearing in connection with this boundedness.
LA - eng
KW - weights; Orlicz spaces; $BMO$; fractional integral; Orlicz space; weighted Orlicz space; space of homogeneous type; fractional integral; Riesz potential
UR - http://eudml.org/doc/249176
ER -

References

top
  1. Bernardis A., Salinas O., Two-weighted inequalities for certain maximal fractional operators on spaces of homogeneous type, Revista de la Unión Matemática Argentina 41 3 (1999). (1999) MR1763261
  2. Genebashvili I., Gogatishvili A., Kokilashvili V., Krbec M., Weight Theory for Integral Transforms on Spaces of Homogeneous Type, Addison Wesley Longman Limited, Harlow, 1998. Zbl0955.42001MR1791462
  3. Gatto A., Vagi S., Fractional integrals on spaces of homogeneous type, Analysis and Partial Differential Equations, Lecture Notes in Pure and Appl. Math., Vol. 122, Marcel Dekker, New York, 1990, pp.171-216. Zbl1002.42501MR1044788
  4. Harboure E., Salinas O., Viviani B., Boundedness of the fractional integral on weighted Lebesgue spaces and Lipschitz spaces, Trans. Amer. Math. Soc. 349 1 (1997), 235-255. (1997) MR1357395
  5. Harboure E., Salinas O., Viviani B., Relations between weighted Orlicz and B M O ( φ ) spaces through fractional integrals, Comment. Math. Univ. Carolinae 40 1 (1999), 53-69. (1999) MR1715202
  6. Kokilashvili V., Krbec M., Weighted Inequalities in Lorentz and Orlicz Spaces, World Scientific, River Edge, NJ, 1991. Zbl0751.46021MR1156767
  7. Macías R., Segovia C., Torrea J., Singular integral operators with non-necessarily bounded kernels on spaces of homogeneous type, Adv. Math. 93 1 (1992). (1992) MR1160842
  8. Macías R., Torrea J., L 2 and L p boundedness of singular integrals on non necessarily normalized spaces of homogeneous type, Cuadernos de Matemática y Mecánica, No. 1-88, PEMA-INTEC-GTM, Santa Fe, Argentina. 
  9. Muckenhoupt B., Wheeden R., Weighted norm inequalities for the fractional integrals, Trans. Amer. Math. Soc. 192 261-274 (1974). (1974) MR0340523
  10. Pradolini G., Two-weighted norm inequalities for the fractional integral operator between L p and Lipschitz spaces, Comment. Math. Prace Mat. 41 (2001), 147-169. (2001) MR1876717
  11. Pradolini G., A class of pairs of weights related to the boundedness of the Fractional Integral Operator between L p and Lipschitz spaces, Comment. Math. Univ. Carolinae 42 (2001), 133-152. (2001) MR1825378
  12. Rao, M.M., Ren Z.D., Theory of Orlicz Spaces, Marcel Dekker, New York, 1991. Zbl0724.46032MR1113700
  13. Sawyer E., A characterization of two-weight norm inequalities related to the fractional and Poisson integrals, Trans. Amer. Math. Soc. 308 533-545 (1988). (1988) MR0930072

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.