Inequalities for Walsh like random variables
Let (Xn)n≥1 be a sequence of mean zero independent random variables. Let Wk={∏j=1kXij|1≤i1<i2…<ik}, Yk=⋃j≤kWj and let [Yk] be the linear span of Yk. Assume δ≤|Xn|≤K for some δ>0 and K>0 and let C(p,m)=16(52p2p−1)m−1plogp(Kδ)m for 1<p<∞. We show that for f∈[Ym] the following inequal...
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| Language: | English |
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Wiley
1990-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171290000527 |
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| author | D. Hajela |
| author_facet | D. Hajela |
| author_sort | D. Hajela |
| collection | DOAJ |
| description | Let (Xn)n≥1 be a sequence of mean zero independent random variables. Let Wk={∏j=1kXij|1≤i1<i2…<ik}, Yk=⋃j≤kWj and let [Yk] be the linear span of Yk. Assume δ≤|Xn|≤K for some δ>0 and K>0 and let C(p,m)=16(52p2p−1)m−1plogp(Kδ)m for 1<p<∞. We show that for f∈[Ym] the following inequalities hold:‖f‖2≤‖f‖p≤C(p,m)‖f‖2 for 2<p<∞‖f‖2≤C(q,m)‖f‖p≤C(q,m)‖f‖2 for 1<p<2, 1p+1q=1and ‖f‖2≤C(4,m)2‖f‖1≤C(4,m)2‖f‖2. These generalize various well known inequalities on Walsh functions. |
| format | Article |
| id | doaj-art-56bf7389948147e4b2744afc564d1a9b |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1990-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-56bf7389948147e4b2744afc564d1a9b2025-02-03T01:31:51ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251990-01-0113235335610.1155/S0161171290000527Inequalities for Walsh like random variablesD. Hajela0Bell Communications Research, 2P-390, 445 South Street, Morristown, New Jersey 07960, USALet (Xn)n≥1 be a sequence of mean zero independent random variables. Let Wk={∏j=1kXij|1≤i1<i2…<ik}, Yk=⋃j≤kWj and let [Yk] be the linear span of Yk. Assume δ≤|Xn|≤K for some δ>0 and K>0 and let C(p,m)=16(52p2p−1)m−1plogp(Kδ)m for 1<p<∞. We show that for f∈[Ym] the following inequalities hold:‖f‖2≤‖f‖p≤C(p,m)‖f‖2 for 2<p<∞‖f‖2≤C(q,m)‖f‖p≤C(q,m)‖f‖2 for 1<p<2, 1p+1q=1and ‖f‖2≤C(4,m)2‖f‖1≤C(4,m)2‖f‖2. These generalize various well known inequalities on Walsh functions.http://dx.doi.org/10.1155/S0161171290000527 |
| spellingShingle | D. Hajela Inequalities for Walsh like random variables International Journal of Mathematics and Mathematical Sciences |
| title | Inequalities for Walsh like random variables |
| title_full | Inequalities for Walsh like random variables |
| title_fullStr | Inequalities for Walsh like random variables |
| title_full_unstemmed | Inequalities for Walsh like random variables |
| title_short | Inequalities for Walsh like random variables |
| title_sort | inequalities for walsh like random variables |
| url | http://dx.doi.org/10.1155/S0161171290000527 |
| work_keys_str_mv | AT dhajela inequalitiesforwalshlikerandomvariables |