This classic of the mathematical literature forms a comprehensive study of the inequalities used throughout mathematics. First published in 1934, it presents clearly and exhaustively both the statement and proof of all the standard inequalities of analysis. The authors were well known for their powers of exposition and were able here to make the subject accessible to a wide audience of mathematicians.
Was andere dazu sagen - Rezension schreiben
Es wurden keine Rezensionen gefunden.
MEAN VALUES WITHAN
VARIOUS APPLICATIONS OF THE CALCULUS
functions ofseveral variables 4 7 Comparisonofseries and integrals 4 8 An inequality of W H Young
11 Minkowskisinequality 2 12 A companion to Minkowskis
Andere Ausgaben - Alle anzeigen
applications arbitrary argument asserts assume bilinear form Calculus Calculus of Variations chapter chord concave consider constant continuous and strictly continuous function convergent convex function corollary correspond to Theorems curve decreases deduce Theorem defined definition denote derivative divergent effectively proportional equality equation equivalent example follows from Theorem forx Fourier series generalisation gives Hence Hilbert’s Hölder’s inequality homogeneous increasing function infinite series inthe Lebesgue Lebesgue integrals lefthand side limit maximum means measure Minkowski’s inequality MISCELLANEOUS THEOREMS monotonic functional multilinear forms necessary and sufficient negative nonnegative null set obtain ofthe ofTheorem positive and finite proof of Theorem properties prove Theorem remarks replace result Riesz righthand side Stieltjes integral strictly monotonic sufficient condition summation Suppose Theorem 13 Theorem 9 theory true unless f values vanishes variational W. H. Young wehave write zero