Nontrivial examples of JNp and VJNp functions
| dc.contributor | Aalto-yliopisto | fi |
| dc.contributor | Aalto University | en |
| dc.contributor.author | Takala, Timo | en_US |
| dc.contributor.department | Department of Mathematics and Systems Analysis | en |
| dc.contributor.groupauthor | Analysis | en |
| dc.contributor.organization | Analysis | en_US |
| dc.date.accessioned | 2022-11-09T08:04:28Z | |
| dc.date.available | 2022-11-09T08:04:28Z | |
| dc.date.issued | 2022-10 | en_US |
| dc.description | Funding Information: Open Access funding provided by Aalto University. The research was funded by Aalto University. Publisher Copyright: © 2022, The Author(s). | |
| dc.description.abstract | We study the John-Nirenberg space JNp, which is a generalization of the space of bounded mean oscillation. In this paper we construct new JNp functions, that increase the understanding of this function space. It is already known that Lp(Q) ⊊ JNp(Q) ⊊ Lp,∞(Q). We show that if | f| 1/p∈ JNp(Q) , then | f| 1/q∈ JNq(Q) , where q≥ p, but there exists a nonnegative function f such that f1/p∉ JNp(Q) even though f1/q∈ JNq(Q) , for every q∈ (p, ∞). We present functions in JNp(Q) \ VJNp(Q) and in VJNp(Q) \ Lp(Q) , proving the nontriviality of the vanishing subspace VJNp, which is a JNp space version of VMO. We prove the embedding JNp(Rn) ⊂ Lp,∞(Rn) / R. Finally we show that we can extend the constructed functions into Rn, such that we get a function in JNp(Rn) \ VJNp(Rn) and another in CJNp(Rn) \ Lp(Rn) / R. Here CJNp is a subspace of JNp that is inspired by the space CMO. | en |
| dc.description.version | Peer reviewed | en |
| dc.format.extent | 27 | |
| dc.format.extent | 1279-1305 | |
| dc.format.mimetype | application/pdf | en_US |
| dc.identifier.citation | Takala, T 2022, ' Nontrivial examples of JN p and VJN p functions ', MATHEMATISCHE ZEITSCHRIFT, vol. 302, no. 2, pp. 1279-1305 . https://doi.org/10.1007/s00209-022-03100-w | en |
| dc.identifier.doi | 10.1007/s00209-022-03100-w | en_US |
| dc.identifier.issn | 0025-5874 | |
| dc.identifier.issn | 1432-1823 | |
| dc.identifier.other | PURE UUID: e1926671-4502-463e-b7e8-76a96924d0b3 | en_US |
| dc.identifier.other | PURE ITEMURL: https://research.aalto.fi/en/publications/e1926671-4502-463e-b7e8-76a96924d0b3 | en_US |
| dc.identifier.other | PURE LINK: http://www.scopus.com/inward/record.url?scp=85136182599&partnerID=8YFLogxK | en_US |
| dc.identifier.other | PURE FILEURL: https://research.aalto.fi/files/91631638/Nontrivial_examples_of_JNp_and_VJNp_functions.pdf | en_US |
| dc.identifier.uri | https://aaltodoc.aalto.fi/handle/123456789/117709 | |
| dc.identifier.urn | URN:NBN:fi:aalto-202211096480 | |
| dc.language.iso | en | en |
| dc.publisher | SPRINGER | |
| dc.relation.ispartofseries | MATHEMATISCHE ZEITSCHRIFT | en |
| dc.relation.ispartofseries | Volume 302, issue 2 | en |
| dc.rights | openAccess | en |
| dc.subject.keyword | Bounded mean oscillation | en_US |
| dc.subject.keyword | Cube | en_US |
| dc.subject.keyword | Euclidian space | en_US |
| dc.subject.keyword | John-Nirenberg inequality | en_US |
| dc.subject.keyword | John–Nirenberg space | en_US |
| dc.subject.keyword | Vanishing subspace | en_US |
| dc.title | Nontrivial examples of JNp and VJNp functions | en |
| dc.type | A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä | fi |
| dc.type.version | publishedVersion |
