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The main theme of the book is the study, from the standpoint of s-numbers, of integral operators of Hardy type and related Sobolev embeddings. In the theory of s-numbers the idea is to attach to every bounded linear map between Banach spaces a monotone decreasing sequence of non-negative numbers with a view to the classification of operators according to the way in which these numbers approach a limit: approximation numbers provide an especially important example of such numbers. The asymptotic behavior of the s-numbers of Hardy operators acting between Lebesgue spaces is determined here in a wide variety of cases. The proof methods involve the geometry of Banach spaces and generalized trigonometric functions; there are connections with the theory of the p-Laplacian.

Eigenvalues --- Embeddings (Mathematics) --- Trigonometrical functions --- Mathematics --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- Algebra --- Applied Mathematics --- Trigonometrical functions. --- Circular functions --- Mathematics. --- Mathematical analysis. --- Analysis (Mathematics). --- Approximation theory. --- Functional analysis. --- Differential equations. --- Special functions. --- Analysis. --- Approximations and Expansions. --- Functional Analysis. --- Special Functions. --- Ordinary Differential Equations. --- Mathematics Education. --- Study and teaching. --- Special functions --- Mathematical analysis --- 517.91 Differential equations --- Differential equations --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Theory of approximation --- Functional analysis --- Functions --- Polynomials --- Chebyshev systems --- 517.1 Mathematical analysis --- Math --- Science --- Transcendental functions --- Global analysis (Mathematics). --- Functions, special. --- Differential Equations. --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Mathematics—Study and teaching .