Weighted estimates for the averaging integral operator

0342853 - MÚ 2011 RIV ES eng J - Journal Article
Opic, Bohumír - Rákosník, Jiří
Weighted estimates for the averaging integral operator.
Collectanea Mathematica. Roč. 61, č. 3 (2010), s. 253-262. ISSN 0010-0757. E-ISSN 2038-4815
R&D Projects: GA ČR GA201/05/2033; GA ČR GA201/08/0383
Institutional research plan: CEZ:AV0Z10190503
Keywords : averaging integral operator * weighted Lebesgue spaces * weights
Subject RIV: BA - General Mathematics
Impact factor: 0.474, year: 2010
http://link.springer.com/article/10.1007%2FBF03191231

Let 1 < p <= q < +infinity and let v, w be weights on (0, +infinity) satisfying" (star) v(x)x(rho) is equivalent to a non-decreasing function on (0, +infinity) for some rho >= 0 and w(x)x](1/q) approximate to [v(x)x](1/p) for all x is an element of (0, +infinity), We prove that if the averaging operator (Af)(x) = 1/x integral(x)(0) f(t)dt, x is an element of (0, +infinity), is bounded from the weighted Lebesgue space L-p(0, +infinity), v) into the weighted Lebesgue space L-q((0, +infinity); w), then there exists epsilon(0) is an element of (0, p - 1) such that the space Lq-epsilon q/p((0, +infinity), w(x)(1+delta)x(delta(1-q/p))x(gamma q/p)) for all epsilon, delta, gamma is an element of [0, epsilon(0)).
Permanent Link: http://hdl.handle.net/11104/0185472