Displaying similar documents to “A limiting case of the uncertainty principle”

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 ≥ 2 . In a well-known paper , 20, 1077–1092 (1971) Moser found the smallest value of K such that sup ∫ Ω exp f ( x ) K n / ( n - 1 ) : f ∈ W 0 1 , n ( Ω ) , ∥ ∇ f ∥ L n ≤ 1 < ∞ . 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.

Explicit lower bounds for linear forms in two logarithms

Nicolas Gouillon (2006)

Journal de Théorie des Nombres de Bordeaux

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We give an explicit lower bound for linear forms in two logarithms. For this we specialize the so-called Schneider method with multiplicity described in []. We substantially improve the numerical constants involved in existing statements for linear forms in two logarithms, obtained from Baker’s method or Schneider’s method with multiplicity. Our constant is around 5 . 10 4 instead of 10 8 .