= 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)).">
= 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)).">
Weighted estimates for the averaging integral operator
$3 cav_un_auth*0100689 $a Opic $b Bohumír $i Topologie a funkcionální analýza $j Topology and Functional Analysis $l TFA $p MU-W $4 070 $T Matematický ústav AV ČR, v. v. i.
701
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$3 cav_un_auth*0100701 $a Rákosník $b Jiří $i Topologie a funkcionální analýza $j Topology and Functional Analysis $l TFA $p MU-W $w Abstract Analysis $4 070 $T Matematický ústav AV ČR, v. v. i.