Products of integral-type and composition operators between generally weighted Bloch spaces.

Li, Haiying; Ma, Tianshui

Displaying similar documents to “Products of integral-type and composition operators between generally weighted Bloch spaces.”

Mean value of Piltz' function over integers free of large prime factors.

Nyandwi, Servat (2003)

Publications de l'Institut Mathématique. Nouvelle Série

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Palindromic powers.

Hernández, Santos Hernández, Luca, Florian (2006)

Revista Colombiana de Matemáticas

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On Robin’s criterion for the Riemann hypothesis

YoungJu Choie, Nicolas Lichiardopol, Pieter Moree, Patrick Solé (2007)

Journal de Théorie des Nombres de Bordeaux

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Robin’s criterion states that the Riemann Hypothesis (RH) is true if and only if Robin’s inequality $σ (n) : = \sum_{d | n} d < e^{γ} n log log n$ is satisfied for $n \geq 5041$ , where $γ$ denotes the Euler(-Mascheroni) constant. We show by elementary methods that if $n \geq 37$ does not satisfy Robin’s criterion it must be even and is neither squarefree nor squarefull. Using a bound of Rosser and Schoenfeld we show, moreover, that $n$ must be divisible by a fifth power $> 1$ . As consequence we obtain that RH holds true iff every natural number divisible by...

A sharp form of an embedding into multiple exponential spaces

Robert Černý, Silvie Mašková (2010)

Czechoslovak Mathematical Journal

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Let $Ω$ be a bounded open set in $ℝ^{n}$ , $n \geq 2$ . In a well-known paper , 20, 1077–1092 (1971) Moser found the smallest value of $K$ such that $sup \{\int_{Ω} exp ({(\frac{|f (x)|}{K})}^{n / (n - 1)}) : f \in W_{0}^{1, n} (Ω), {∥ \nabla f ∥}_{L^{n}} \leq 1\} < \infty .$ We extend this result to the situation in which the underlying space $L^{n}$ is replaced by the generalized Zygmund space $L^{n} {log}^{n - 1} L {log}^{α} log L$ $(α < n - 1)$ , the corresponding space of exponential growth then being given by a Young function which behaves like $exp (exp (t^{n / (n - 1 - α)}))$ for large $t$ . We also discuss the case of an embedding into triple and other multiple exponential cases.