The systematic treatment of spaces with weights began at the end of the fifties. The main field of application are the degenerate (elliptic) differential operators. There are only very few papers which are concerned with the interpolation theory of these spaces. In this paper, we use the interpolation method introduced by Gustavsson-Peetre [Stud. Math. 60 (1977) 33] to interpolate between weighted L-p-spaces. Here, we shall give some fundamental definitions and the basic interpolation results for the real interpolation method <(X) over right arrow >(rho) introduced in [Stud. Math. 60 (1977) 33] (see [SWJPAM 2 (1997) 29] and [SWJPAM 1 (2002) 71]). We also prove certain variants of two classical inequalities (Carlson's inequality and Khinchine's inequality) which will be needed later. We introduce our interpolation spaces <(L) over right arrow (Phi) (w)>(rho) and finally, we prove our main results. (C) 2003 Published by Elsevier Inc.
机构:
Balikesir Univ, Fac Art & Sci, Dept Math, TR-10145 Balikesir, TurkeyBalikesir Univ, Fac Art & Sci, Dept Math, TR-10145 Balikesir, Turkey
Akgun, Ramazan
Israfilov, Daniyal M.
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Balikesir Univ, Fac Art & Sci, Dept Math, TR-10145 Balikesir, Turkey
ANAS Inst Math & Mech Baku, Baku, AzerbaijanBalikesir Univ, Fac Art & Sci, Dept Math, TR-10145 Balikesir, Turkey
机构:
Univ Alabama, Dept Math, Tuscaloosa, AL 35487 USAUniv Alabama, Dept Math, Tuscaloosa, AL 35487 USA
Cruz-Uribe, David
Hasto, Peter
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Univ Oulu, Dept Math Sci, POB 3000, FI-90014 Oulu, Finland
Univ Turku, Dept Math & Stat, FI-20014 Turku, FinlandUniv Alabama, Dept Math, Tuscaloosa, AL 35487 USA