PARABOLIC FRACTIONAL MAXIMAL OPERATOR IN PARABOLIC GENERALIZED MORREY SPACES
Yazarlar (2)
Prof. Dr. Vagıf GULIYEV
Kirsehir Ahi Evran University, Türkiye
Ministry of Education of Azerbaijan Republic, Azerbaycan
| Makale Türü | Özgün Makale (ESCI dergilerinde yayınlanan tam makale) | ||
| Dergi Adı | PROCEEDINGS OF THE INSTITUTE OF MATHEMATICS AND MECHANICS | ||
| Dergi ISSN | 2409-4986 Wos Dergi Scopus Dergi | ||
| Makale Dili | İngilizce | Basım Tarihi | 01-2012 |
| Cilt / Sayı / Sayfa | 37 / 45 / 51–66 | DOI | – |
| Özet |
| We study the parabolic fractional maximal operator M-alpha(P), 0 <= alpha < gamma in the parabolic generalized Morrey space M-P,M-phi, P(R-n), where gamma = trP is the homogeneous dimension on R-n. We find the conditions on the pair (phi(1), phi(2)) which ensures the boundedness of the operator MP a from one generalized Morrey space M-P,M-phi 1, P(R-n) to another M-P,M-phi 2, P (R-n), 1 < p <= q < infinity, 1/p - 1/q = alpha/gamma, and from the space M-P,M-phi 1, P (R-n) to the weak space WMq,phi 2, P (R-n), 1 <= q < infinity, 1 - 1/q = alpha/gamma. Also find conditions on the f which ensure the Adams type boundedness of the M alpha(P) from M-p,M-phi 1/p, P (R-n) to M-q,M-phi 1/q, (R-n) for 1 < p < q < infinity and from M-1,M-phi,(P) (R-n) to WMq,phi 1/q, P (R-n) for 1 < q < infinity. In the case b is an element of BMOP (R-n) and 1 < p < q < infinity, find the sufficient conditions on the pair (phi(1), phi(2)) which ensures the boundedness of the commutator operator M-b,alpha(P) from M-p,M-phi 1, (P) (R-n) to M-q,M- phi 2,M- P (R-n) with 1/p - 1/q = alpha/gamma. Also find the sufficient conditions on the f which ensures the boundedness of the operator M-b,M-alpha (P) from M-p,M- phi 1/P (R-n) to M-q,(phi 1/q), (P) (R-n) for 1 < p < q < infinity. As an application, we establish the boundedness of some Schr " odinger type operators on parabolic generalized Morrey spaces related to certain nonnegative potentials belonging to the reverse Holder class. |
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