General reiteration theorems for R and L classes: Case of left R-spaces and right

Some Reiteration Theorems for R , L , R R , Doktorski1 2021Journal of Function Spaces

“…We introduce here four interpolation spaces. We follow [6][7][8] where it has been shown that they appear in relation to the extreme reiteration results.…”

“…Theorem 20 (cf. [6], Theorem 4.8 (b, c)). Let 0 Put χ 1 ðtÞ = a 1 ðtÞ ks −1/r 1 b 1 ðsÞk r 1 ,ðt,∞Þ and ρðtÞ = t θ 1 ðks −1/r 0 b 0 ðsÞk r 0 ,ðt,∞Þ /χ 1 ðtÞÞ.…”

“…The motivation for this work was the articles [6][7][8], where it has been shown that for some limiting combinations of parameters, new interpolation spaces are required. Following [6,7], we call them LL, LR, RL, and RR extremal…”

“…The author is grateful to Pedro Fernández-Martínez and Teresa Signes for the possibility to read the paper [8] before it was posted in arXiv and for the productive discussion about our papers. We address a grateful thanks to Teresa Signes for pointing out a wrong statement in [5].…”

“…and by (16), Theorem 35 (cf. [8], Theorem 3.4). Let 0 < θ 0 < θ 1 < 1, 0 < q 0 , r 0 , q 1 , r 1 ≤ ∞, a 0 , b 0 , a 1 , b 1 ∈ SV, ks −1/r 0 b 0 ðsÞk r 0 ,ð1,∞Þ < ∞, and ks −1/r 1 b 1 ðsÞk r 1 ,ð0,1Þ < ∞.…”