Geodesic
Boundedness of one-sided fractional integrals in the one-sided Calderón-Hardy spaces
Commentationes Mathematicae Universitatis Carolinae, Tome 52 (2011) no. 1, pp. 57-75.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

In this paper we study the mapping properties of the one-sided fractional integrals in the Calderón-Hardy spaces $\mathcal{H}_{q,\alpha}^{p,+}(\omega)$ for $0 p\leq 1$, $0 \alpha \infty $ and $1 q \infty $. Specifically, we show that, for suitable values of $p,q,\gamma, \alpha$ and $s$, if $\omega \in A_s^+$ (Sawyer's classes of weights) then the one-sided fractional integral $I_{\gamma }^+$ can be extended to a bounded operator from $\mathcal{H}_{q,\alpha}^{p,+}(\omega)$ to $\mathcal{H}_{q,\alpha + \gamma}^{p,+}(\omega)$. The result is a consequence of the pointwise inequality $$ N_{q, \alpha +\gamma}^+\left( I_{\gamma }^+ F;x\right) \leq C_{\alpha,\gamma } N_{q, \alpha}^+ \left( F;x\right), $$ where $N_{q, \alpha}^+ (F;x)$ denotes the Calderón maximal function.
Classification : 42B20, 42B35
Keywords: fractional integral; maximal; one-sided Calderón-Hardy; one-sided weights spaces 
@article{CMUC_2011__52_1_a4,
     author = {Perini, Alejandra},
     title = {Boundedness of one-sided fractional integrals in the one-sided {Calder\'on-Hardy} spaces},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {57--75},
     publisher = {mathdoc},
     volume = {52},
     number = {1},
     year = {2011},
     mrnumber = {2828370},
     zbl = {1240.42061},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2011__52_1_a4/}
}
TY  - JOUR
AU  - Perini, Alejandra
TI  - Boundedness of one-sided fractional integrals in the one-sided Calderón-Hardy spaces
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 2011
SP  - 57
EP  - 75
VL  - 52
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMUC_2011__52_1_a4/
LA  - en
ID  - CMUC_2011__52_1_a4
ER  - 
%0 Journal Article
%A Perini, Alejandra
%T Boundedness of one-sided fractional integrals in the one-sided Calderón-Hardy spaces
%J Commentationes Mathematicae Universitatis Carolinae
%D 2011
%P 57-75
%V 52
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMUC_2011__52_1_a4/
%G en
%F CMUC_2011__52_1_a4
Perini, Alejandra. Boundedness of one-sided fractional integrals in the one-sided Calderón-Hardy spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 52 (2011) no. 1, pp. 57-75. http://geodesic.mathdoc.fr/item/CMUC_2011__52_1_a4/