Boundedness and unboundedness results for some maximal operators on functions of bounded variation

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:337

Article

Aldaz, J. M.¹  Lazaro, J. Perez^1,2 

[1] Univ La Rioja, Dept Matemat & Comp, Logrona 26004, La Rioja, Spain

[2] Univ Publ Navarra, Dept Matemat & Informat, Pamplona 31006, Navarra, Spain

关键词: maximal function;    Sobolev spaces;    bounded variation functions;   

DOI  :  10.1016/j.jmaa.2007.03.097

来源: Elsevier

【 摘 要 】

We characterize the space BV(I) of functions of bounded variation on an arbitrary interval I subset of R, in terms of a uniform boundedness condition satisfied by the local uncentered maximal operator M-R from BV(I) into the Sobolev space W-1,W-1(I). By restriction, the corresponding characterization holds for W-1,W-1(I). We also show that if U is open in R-d, d > 1, then boundedness from BV(U) into W-1,W-1(U) fails for the local directional maximal operator M-T(v) the local strong maximal operator M-T(S), and the iterated local directional maximal operator M-T(d) o...o M-T(1). Nevertheless, if U satisfies a cone condition, then M-T(S):BV(U) -> L-1(U) boundedly, and the same happens with M-T(v), M-T(d) o...o M-T(1), and M-R. (C) 2007 Elsevier Inc. All rights reserved.

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