Bojanov-Naidenov problem for positive (negative) parts of differentiable functions on the real domain

V.V. Kameneva (Oles Honchar Dnipro National University)
V.A. Kofanov (Oles Honchar Dnipro National University),


We solve the extremal problem $$$\| x^{(k)}_{\pm} \|_{L_p[a,b]} \rightarrow \sup$$$, $$$k = 0, 1, ..., r-1$$$, over the set of pairs $$$(x, I)$$$ of functions $$$x\in W^r_{\infty} (\mathbb{R})$$$ and intervals $$$I = [a,b]$$$ with restrictions on the local norm of function $$$x$$$ and the measure of support $$$\mu \{ \mathrm{supp}_{[a,b]} x^{(k)}_{\pm} \}$$$.


Bojanov-Naidenov problem; positive (negative) part of function; rearrangement; comparison theorem


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ISSN (Online): 2664-5009
ISSN (Print): 2664-4991