An Odd Rearrangement of L1(Rn)
We introduce an odd rearrangement f* defined by π(f)(x)=f*(x)=sgn(x1)f*(νn|x|n), x∈Rn, where f* is a decreasing rearrangement of the measurable function f. With the help of this odd rearrangement, we show that for each f∈L1(Rn), there exists a g∈H1(Rn) such that df=dg, where df is an distribution fu...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
|
| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2014/787840 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832564712615706624 |
|---|---|
| author | Zheng Wang Jiecheng Chen |
| author_facet | Zheng Wang Jiecheng Chen |
| author_sort | Zheng Wang |
| collection | DOAJ |
| description | We introduce an odd rearrangement f* defined by π(f)(x)=f*(x)=sgn(x1)f*(νn|x|n), x∈Rn, where f* is a decreasing rearrangement of the measurable function f. With the help of this odd rearrangement, we show that for each f∈L1(Rn), there exists a g∈H1(Rn) such that df=dg, where df is an distribution function of f. Moreover, we study the boundedness of singular integral operators when they are restricted to odd rearrangement of L1(Rn), and we give some results on Hilbert transform. |
| format | Article |
| id | doaj-art-d28a7ed733e545fe97eeb98fbe52fd3c |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-d28a7ed733e545fe97eeb98fbe52fd3c2025-02-03T01:10:26ZengWileyJournal of Function Spaces2314-88962314-88882014-01-01201410.1155/2014/787840787840An Odd Rearrangement of L1(Rn)Zheng Wang0Jiecheng Chen1Department of Mathematics, Zhejiang University, Hangzhou 310027, ChinaDepartment of Mathematics, Zhejiang Normal University, Jinhua 321004, ChinaWe introduce an odd rearrangement f* defined by π(f)(x)=f*(x)=sgn(x1)f*(νn|x|n), x∈Rn, where f* is a decreasing rearrangement of the measurable function f. With the help of this odd rearrangement, we show that for each f∈L1(Rn), there exists a g∈H1(Rn) such that df=dg, where df is an distribution function of f. Moreover, we study the boundedness of singular integral operators when they are restricted to odd rearrangement of L1(Rn), and we give some results on Hilbert transform.http://dx.doi.org/10.1155/2014/787840 |
| spellingShingle | Zheng Wang Jiecheng Chen An Odd Rearrangement of L1(Rn) Journal of Function Spaces |
| title | An Odd Rearrangement of L1(Rn) |
| title_full | An Odd Rearrangement of L1(Rn) |
| title_fullStr | An Odd Rearrangement of L1(Rn) |
| title_full_unstemmed | An Odd Rearrangement of L1(Rn) |
| title_short | An Odd Rearrangement of L1(Rn) |
| title_sort | odd rearrangement of l1 rn |
| url | http://dx.doi.org/10.1155/2014/787840 |
| work_keys_str_mv | AT zhengwang anoddrearrangementofl1rn AT jiechengchen anoddrearrangementofl1rn AT zhengwang oddrearrangementofl1rn AT jiechengchen oddrearrangementofl1rn |