Let Formula Presented the weight function on Formula Presented denote the space of even integrable functions on ℝ with respect to Formula Presented and define the radial maximal operator Formula Presented, as usual. We introduce a real Hardy space H1(Δ) as the set of all even locally integrable functions f on ℝ whose radial maximal function Formula Presented belongs to L1(Δ). We shall obtain a relation between H1(Δ) and H1(ℝ). As an application of H1(Δ), we shall consider (H1(Δ),L1(Δ)) boundedness of integral operators associated to the Poisson kernel for Jacobi analysisj the Poisson maximal operator Formula Presented, the Littlewood-Paley g-function, and the Lusin area function S. They are bounded on Lp(Δ) for p >1, but not true for p = 1. We shall prove that Formula Presented, g, and a modified Formula Presented are bounded form H1(Δ) to L1(Δ).
|Title of host publication||Infinite Dimensional Harmonic Analysis IV: On the Interplay Between Representation Theory, Random Matrices, Special Functions, and Probability|
|Publisher||World Scientific Publishing Co.|
|Number of pages||14|
|ISBN (Print)||9812832815, 9789812832818|
|Publication status||Published - 2008 Jan 1|
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