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...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2014/787840 |
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| Summary: | 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. |
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| ISSN: | 2314-8896 2314-8888 |