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Let m and n be positive integers with n 2 and 1 m n ? 1. We study rearrangement-invariant quasinorms % R and % D on functions f : (0; 1) ! R such that to each bounded domain in R n , with Lebesgue measure jj, there corresponds C = C(jj) > 0 for which one has the Sobolev imbedding inequality % R ? u (jjt) C% D ? jr m uj (jjt) ; u 2 C m 0 ((); involving the(More)
In this survey we shall explore (one definition of) generalized trigonometric functions from different standpoints and illustrate the roles they play in various branches of mathematics. We start from the analytic point of view and for each p ∈ (1, ∞) introduce a function sin −1 p by an integral formula, which is just an extension of the well known integral(More)
In [l] it is shown that barrelledness and quasi-barrelledness are merely the two extreme examples of a property, called 2-symmetry, which may be possessed by a locally convex Hausdorff topological vector space. The object of this note is to show how recent char-acterisations [2; 3] of barrelled and quasi-barrelled spaces may be subsumed under(More)