TY  - JOUR
AU  - Betancor, J.J.
AU  - Stempak, K.
T1  - On Hankel conjugate functions
LA  - eng
PY  - 2004
SP  - 59
EP  - 91
T2  - Studia Scientiarum Mathematicarum Hungarica
SN  - 0081-6906
VL  - 41
IS  - 1
AB  - We consider some aspects of harmonic analysis of the differential operator ℒν = -d2/dx2 + (ν2-1/4)/ x2, ν > -1. Spectral decomposition of its self-adjoint extension is given in terms of the Hankel transform Hν. We present a fairly detailed analysis of the corresponding Poisson semigroup {P t}t>0: this is given in a weighted setting with A p-weights involved. Then, we consider conjugate Poisson integrals of functions from Lp(w), w ∈ Ap, 1 ≦ p < ∞. Boundary values of the conjugate Poisson integrals exist both in L p(w) and a.e., and the resulting mapping is called the generalized Hubert transform. Mapping properties of that transform are then proved. All this complements, in some sense, the analysis of conjugacy for the modified Hankel transform Hv which was initiated in the classic paper of Muckenhoupt and Stein, then continued in a series of papers by Andersen, Kerman, Rooney and others.
DO  - 10.1556/SSCMATH.41.2004.1.4
UR  - https://portalciencia.ull.es/documentos/5e3add08299952629a024cc3
DP  - Dialnet - Portal de la Investigación
ER  -