Geodesic
Weak and strong type estimates for fractional integral operators on Morrey spaces over metric measure spaces
Eurasian mathematical journal, Tome 4 (2013) no. 1, pp. 76-81.

Voir la notice de l'article provenant de la source Math-Net.Ru

We discuss here a weak and strong type estimate for fractional integral operators on Morrey spaces over metric measure spaces, where the underlying measure does not always satisfy the doubling condition. 
@article{EMJ_2013_4_1_a6,
     author = {I. Sihwaningrum and Y. Sawano},
     title = {Weak and strong type estimates for fractional integral operators on {Morrey} spaces over metric measure spaces},
     journal = {Eurasian mathematical journal},
     pages = {76--81},
     publisher = {mathdoc},
     volume = {4},
     number = {1},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EMJ_2013_4_1_a6/}
}
TY  - JOUR
AU  - I. Sihwaningrum
AU  - Y. Sawano
TI  - Weak and strong type estimates for fractional integral operators on Morrey spaces over metric measure spaces
JO  - Eurasian mathematical journal
PY  - 2013
SP  - 76
EP  - 81
VL  - 4
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/EMJ_2013_4_1_a6/
LA  - en
ID  - EMJ_2013_4_1_a6
ER  - 
%0 Journal Article
%A I. Sihwaningrum
%A Y. Sawano
%T Weak and strong type estimates for fractional integral operators on Morrey spaces over metric measure spaces
%J Eurasian mathematical journal
%D 2013
%P 76-81
%V 4
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/EMJ_2013_4_1_a6/
%G en
%F EMJ_2013_4_1_a6
I. Sihwaningrum; Y. Sawano. Weak and strong type estimates for fractional integral operators on Morrey spaces over metric measure spaces. Eurasian mathematical journal, Tome 4 (2013) no. 1, pp. 76-81. http://geodesic.mathdoc.fr/item/EMJ_2013_4_1_a6/

[1] D. Adams, “A note on Riesz potentials”, Duke Math. J., 42 (1975), 765–778 | DOI | MR | Zbl

[2] G. H. Hardy, J. E. Littlewood, “Some properties of fractional integrals, I”, Math. Zeit., 27 (1927), 565–606 | DOI | MR

[3] G. H. Hardy, J. E. Littlewood, “Some properties of fractional integrals, II”, Math. Zeit., 34 (1932), 403–439 | DOI | MR

[4] L. I. Hedberg, “On certain convolution inequalities”, Proc. Amer. Math. Soc., 36 (1972), 505–510 | DOI | MR

[5] G. Liu, L. Shu, “Boundedness for the commutator of fractional integral on generalized Morrey space in nonhomogenous space”, Anal. Theory Appl., 27 (2011), 51–58 | DOI | MR | Zbl

[6] E. Nakai, “Hardy–Littlewood maximal operator, singular integral operators, and the Riesz potentials on generalized Morrey spaces”, Math. Nachr., 166 (1994), 95–103 | DOI | MR | Zbl

[7] F. Nazarov, S. Treil, A. Volberg, “Weak type estimates and Cotlar inequalities for Calderon–Zygmund operators on non-homogeneous spaces”, Internat. Math. Res. Notices, 9 (1998), 463–487 | DOI | MR | Zbl

[8] Y. Sawano, “Sharp estimates of the modified Hardy–Littlewood maximal operator on the nonhomogeneous space via covering lemmas”, Hokkaido Math. J., 34 (2005), 435–458 | DOI | MR | Zbl

[9] Y. Sawano, T. Shimomura, “Sobolev embeddings for Riesz potentials of functions in non-doubling Morrey spaces of variable exponents”, Collectanea Mathematica (online)

[10] Amer. Math. Soc. Transl. ser. 2, 34 (1963), 39–68 | Zbl

[11] Y. Terasawa, “Outer measures and weak type (1,1) estimates of Hardy–Littlewood maximal operators”, J. Inequal. Appl., 2006, 15063, 13 pp. | MR | Zbl