In this paper we deal with a theoretical question raised in connection with the application of Dirichlet-Sch type inequality, obtained by Huang (Int. Math. J. 27(02):1650009, 2016), which has been already applied to obtain multiplicity results for boundary value problems in several recent papers. We also discuss a particular case of it in more detail. As an application, we deduce the least harm...

Abstract In this work we study d-dimensional majorant properties. We prove that a set of frequencies in $\mathbb{Z}^d$ satisfies the strict property on $L^p([0,1]^d)$ for all p > 0 if and only is affinely independent. further construct three types violations property. Any at least d + 2 violates an open interval $p \not\in 2\mathbb{N}$ length 2. infinite sequence intervals Finally, given...

We establish distributional limit theorems for the shape statistics of a concave majorant (i.e. fluctuations its length, supremum, time it is attained and value at T) Lévy process on [0,T] as T→∞. The scale length other statistics, well their asymptotic dependence, vary significantly with tail behaviour measure. key tool in proofs recent representation all processes using stick-breaking represe...

We study mappings satisfying the so-called inverse Poletsky inequality. Under integrability of corresponding majorant, it is proved that these are logarithmic Hölder continuous in neighborhood boundary points. In particular, indicated properties hold for homeomorphisms whose satisfy weighted

We solve the problem of finding optimal entire approximations of prescribed exponential type (unrestricted, majorant and minorant) for a class of truncated and odd functions with a shifted exponential subordination, minimizing the L1(R)-error. The class considered here includes new examples such as the truncated logarithm and truncated shifted power functions. This paper is the counterpart of t...