| Abstrakt: |
In this paper, we explore the boundedness of multilinear Dunkl multipliers in three different cases. Firstly, we prove that under summation Hörmander conditions, multilinear Dunkl multipliers have L p (d w) boundedness in the space L r a d , > 0 p 1 (d w) × L r a d , > 0 p 2 (d w) × ⋯ × L r a d , > 0 p N (d w) , where 1 ≤ p i , p ≤ ∞ , and 1 p 1 + 1 p 2 + ⋯ + 1 p N = 1 p . Secondly, by proving the norm of a specific Carleson measure, we demonstrate that under restricted general Hörmander conditions, the L 1 (d w) boundedness of multilinear Dunkl multipliers can be achieved in the space L r a d , > 0 2 (d w) × L r a d , > 0 2 (d w) × ⋯ × L r a d , > 0 ∞ . Finally, by proving the Littlewood-Paley inequality under Dunkl transforms, we further establish that under general Hörmander conditions, the L p (d w) boundedness of multilinear Dunkl multipliers can be attained in the space L rad p 1 (d w) × L rad p 2 (d w) × ⋯ × L rad p N (d w) , where 2 < p 1 ,... , p N < ∞ , 1 < p < ∞ , and 1 p 1 + 1 p 2 + ⋯ + 1 p N = 1 p . [ABSTRACT FROM AUTHOR] |
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