BOUNDED ANALYTIC FUNCTIONS
CONTENTS I PRELIMINARIES 1 SCHWARZ’S LEMMA 2 PICK’S THEOREM 3 POISSON INTEGRALS 4 HARDY–LITTLEWOOD MAXIMAL FUNCTION 5 NONTANGENTIAL MAXIMAL FUNCTION AND FATOU’S THEOREM 6 SUBHARMONIC FUNCTIONS NOTES EXERCISES AND FURTHER RESULTS II H P SPACES 1 DE?NITIONS 2 BLASCHKE PRODUCTS 3 MAXIMAL FUNCTIONS AND BOUNDARY VALUES 4 (1/?) (LOG | F (T)|/(1 + T2))DT >?? 5 THE NEVANLINNA CLASS 6 INNER FUNCTIONS 7 BEURLING’S THEOREM III CONJUGATE FUNCTIONS 1 PRELIMINARIES 2 THE L P THEOREMS 3 CONJUGATE FUNCTIONS AND MAXIMAL FUNCTIONS IV SOME EXTREMAL PROBLEMS 1 DUAL EXTREMAL PROBLEMS 2 THE CARLESON–JACOBS THEOREM 3 THE HELSON–SZEG¨O THEOREM 4 INTERPOLATING FUNCTIONS OF CONSTANT MODULUS 5 PARAMETRIZATION OF K 6 NEVANLINNA’S PROOF V SOME UNIFORM ALGEBRA 1 MAXIMAL IDEAL SPACES 2 INNER FUNCTIONS 3 ANALYTIC DISCS IN FIBERS 4 REPRESENTING MEASURES AND ORTHOGONAL MEASURES 5 THE SPACE L1/H VI BOUNDED MEAN OSCILLATION 1 PRELIMINARIES 2 THE JOHN–NIRENBERG THEOREM 3 LITTLEWOOD–PALEY INTEGRALS AND CARLESON MEASURES 4 FEFFERMAN’S DUALITY THEOREM 5 VANISHING MEAN OSCILLATION 6 WEIGHTED NORM INEQUALITIES VII INTERPOLATING SEQUENCES 1 CARLESON’S INTERPOLATION THEOREM 2 THE LINEAR OPERATOR OF INTERPOLATION 3 GENERATIONS 4 HARMONIC INTERPOLATION 5 EARL’S ELEMENTARY PROOF VIII THE CORONA CONSTRUCTION 1 INHOMOGENEOUS CAUCHY–RIEMANN EQUATIONS 2 THE CORONA THEOREM 3 TWO THEOREMS ON MINIMUM MODULUS 4 INTERPOLATING BLASCHKE PRODUCTS 5 CARLESON’S CONSTRUCTION 6 GRADIENTS OF BOUNDED HARMONIC FUNCTIONS 7 A CONSTRUCTIVE SOLUTION OF ?B/?¯Z = ? IX DOUGLAS ALGEBRAS 1 THE DOUGLAS PROBLEM 2 H ?+ C 3 THE CHANG-MARSHALL THEOREM 4 THE STRUCTURE OF DOUGLAS ALGEBRAS 5 THE LOCAL FATOU THEOREM AND AN APPLICATION X INTERPOLATING SEQUENCES AND MAXIMAL IDEALS 1 ANALYTIC DISCS IN M 2 HOFFMAN’S THEOREM 3 APPROXIMATE DEPENDENCE BETWEEN KERNELS 4 INTERPOLATING SEQUENCES AND HARMONIC SEPARATION 5 A CONSTRUCTIVE DOUGLAS–RUDIN THEOREM BIBLIOGRAPHY