%0 Journal Article
%T Locally Defined Operators and Locally Lipschitz Composition Operators in the Space <i>WBV</i><i>p</i>(·)([a, b])
%A Jos¨¦ Atilio Guerrero
%A Odalis Mej¨ªa
%A Nelson Merentes
%J Advances in Pure Mathematics
%P 727-744
%@ 2160-0384
%D 2016
%I Scientific Research Publishing
%R 10.4236/apm.2016.610059
%X We give a neccesary and sufficient condition on a function&nbsp;<img src=\"Edit_e55eaad8-3e48-4960-80a1-2c90ab601485.bmp\" alt=\"\" />such that the composition operator (Nemytskij Operator) <em>H</em> defined by <img src=\"Edit_19bc3ee9-3feb-4ea9-819b-362a0335af8d.bmp\" alt=\"\" /> acts in the space<img src=\"Edit_c1b352f8-dd17-47fc-a4d9-f1197d517a42.bmp\" alt=\"\" /> and satisfies a local Lipschitz condition. And, we prove that every locally defined operator mapping the space of continuous and bounded Wiener <em>p</em>(<span style=\"white-space:nowrap;\">&amp;#183;</span>)-variation with variable exponent functions into itself is a Nemytskij com-position operator.
%K Generalized Variation
%K &lt
%K i&gt
%K p&lt
%K /i&gt
%K (&#183
%K )-Variation in Wiener¡¯s Sense
%K Variable Exponent
%K Convergence
%K Helly¡¯s Theorem
%K Local Operator
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=70894