A supplement to the paper “The countable partition averaging operator with respect to a minimal rearrangement invariant ideal of the space $L_1(0,1)$”
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part XV, Tome 149 (1986), pp. 137-141
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Let $\mathcal A$ be a countable partition of $[0,1]$ whose elements have positive measure. For $f\in L_1(0,1)$ the symbol $N_f$ denotes the smallest rearrangement invariant ideal sublattice of $L_1(0,1)$ containing $f$. Conditions are given under which $E(N_f|\mathcal A)\subset N_g$ for some $g\in L_1(0,1)$. It is also stated that $E(f|\mathcal A)\prec 2^5E(f^*|\mathcal A^*)$, where $\prec$ is the Hardy–Littlewood preorder on $L_1(0, 1)$ and $\mathcal A^*$ is a decreasing rearrangement of $\mathcal A$.
@article{ZNSL_1986_149_a11,
author = {A. A. Mekler},
title = {A~supplement to the paper {{\textquotedblleft}The} countable partition averaging operator with respect to a~minimal rearrangement invariant ideal of the space $L_1(0,1)${\textquotedblright}},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {137--141},
year = {1986},
volume = {149},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1986_149_a11/}
}
TY - JOUR AU - A. A. Mekler TI - A supplement to the paper “The countable partition averaging operator with respect to a minimal rearrangement invariant ideal of the space $L_1(0,1)$” JO - Zapiski Nauchnykh Seminarov POMI PY - 1986 SP - 137 EP - 141 VL - 149 UR - http://geodesic.mathdoc.fr/item/ZNSL_1986_149_a11/ LA - ru ID - ZNSL_1986_149_a11 ER -
%0 Journal Article %A A. A. Mekler %T A supplement to the paper “The countable partition averaging operator with respect to a minimal rearrangement invariant ideal of the space $L_1(0,1)$” %J Zapiski Nauchnykh Seminarov POMI %D 1986 %P 137-141 %V 149 %U http://geodesic.mathdoc.fr/item/ZNSL_1986_149_a11/ %G ru %F ZNSL_1986_149_a11
A. A. Mekler. A supplement to the paper “The countable partition averaging operator with respect to a minimal rearrangement invariant ideal of the space $L_1(0,1)$”. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part XV, Tome 149 (1986), pp. 137-141. http://geodesic.mathdoc.fr/item/ZNSL_1986_149_a11/