On Hardy-Type Inequalities and Hankel Transforms

 For the real Hardy spaces , we shall show the Hardy type integral inequalities, and applying the inequalities we shall establish the Hardy’s inequalities with respect to Hankel transforms. Received 21 October 1997; in revised form 19 October 1998     

Inequalities for Discrete Hardy Spaces

We show the molecular characterization of the discrete Hardy spaces and its applications — the molecular characterization proofs of the Marcinkiewicz multiplier theorem and the inequality of fractional integrals for the discrete Hardy spaces.     

Laguerre and Disk Polynomial Expansions with Nonnegative Coefficients

We establish Wiener type theorems and Paley type theorems for Laguerre polynomial expansions and disk polynomial expansions with nonnegative coefficients.     

Paley's Inequality for the Jacobi Expansions

Let be an analytic function in the unit disc satisfying Then, which is familiar as Paley's inequality. In this paper, an analogue of this inequality withrespect to the Jacobi expansions is established.     

Hardy's Inequalities for Hermite and Laguerre Expansions

The well-known inequality of Hardy for Fourier coefficientsof functions in the real Hardy space is . We shall establish analogues of this inequality for the Hermite function expansionsand also for the Laguerre function expansions. 1991 MathematicsSubject Classification 42C10, 33C45.