| On respresentation of derivatives of functions in $L_p$ |
| Miloš Tomić |
Abstract A theorem on the expansion of the derivative $f^{(r_1,r_2,\dots,r_n)}$, where $f\in L_p$, and the derivatives of singular integrals into the series of band-limited functions (entire functions of exponential type), which converges in $L_p$ for $1\le p\le q<\infty$, is proved. The norms of their items are estimated by best approximations by ``an angle''.
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Keywords: Approximation by an angle. |
MSC: 42B99 |
Pages: 235$-$250 |
Volume 62 , Issue 3 , 2010 |
