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There are many tests for determining the convergence or divergence of series. The test of Raabe and the test of Betrand are relatively unknown and do not appear in most classical courses of analysis. Also, the link between these tests and regular variation is seldomly made. In this paper we offer a unified approach to some of the classical tests from a point of view of regular varying sequences.
We survey the connections between extreme-value theory and regular variation, in one and higher dimensions, from the algebraic point of view of our recent work on Popa groups.
In this paper, we first establish the weighted compactness result for oscillation and variation associated with the truncated commutator of singular integral operators. Moreover, we establish a new $CMO(mathbb{R}^n)$ characterization via the compactn
This paper gives the pointwise sparse dominations for variation operators of singular integrals and commutators with kernels satisfying the $L^r$-H{o}rmander conditions. As applications, we obtain the strong type quantitative weighted bounds for such
We prove the recent conjecture that Minkowskis question mark measure is regular, in the sense of Ullman-Stahl-Totik.
Let $mathcal{H}_{alpha}=Delta-(alpha-1)|x|^{alpha}$ be an $[1,infty) ialpha$-Hermite operator for the hydrogen atom located at the origin in $mathbb R^d$. In this paper, we are motivated by the classical case $alpha=1$ to investigate the space of fun