We define new integral operators on the Haydy space similar to Szeg<span style="white-space:nowrap;"><span style="white-space:nowrap;">ö<span style="font-family:Verdana...We define new integral operators on the Haydy space similar to Szeg<span style="white-space:nowrap;"><span style="white-space:nowrap;">ö<span style="font-family:Verdana;"> projection. We show that these operators map from <span style="font-family:Verdana;">H<sup><i style="white-space:normal;"><span style="font-family:Verdana;">p</sup><span style="font-family:Verdana;"> <span style="font-family:Verdana;">to <span style="font-family:Verdana;">H<span style="font-family:Verdana;"><sup><span style="white-space:normal;font-family:Verdana;">2 </sup><span style="font-family:Verdana;">for some 1 <span style="font-family:Verdana;">≤ <span style="font-family:Verdana;">p < <span style="font-family:Verdana;">2, where the range of <span style="font-family:Verdana;">p <span style="font-family:CMR10;"><span style="font-family:Verdana;">is depending on a growth condition. To prove that, we generalize the Hausdorff-Young Theorem to multi-dimensional case.展开更多
The weak-type (1, 1) boundedness of the higher order Riesz-Laguerre transforms associated with the Laguerre polynomials and the boundedness for the Riesz-Laguerre transforms of order 2 are considered. We discuss a pol...The weak-type (1, 1) boundedness of the higher order Riesz-Laguerre transforms associated with the Laguerre polynomials and the boundedness for the Riesz-Laguerre transforms of order 2 are considered. We discuss a polynomial weight w that makes the Riesz-Laguerre transforms of order greater than or equal to 2 continuous from L<sup>1</sup> (wdμ<sub>α</sub>) into L<sup>1,∞</sup> (dμ<sub>α</sub>), under specific value α, where μα</sub> is the Laguerre measure.展开更多
文摘We define new integral operators on the Haydy space similar to Szeg<span style="white-space:nowrap;"><span style="white-space:nowrap;">ö<span style="font-family:Verdana;"> projection. We show that these operators map from <span style="font-family:Verdana;">H<sup><i style="white-space:normal;"><span style="font-family:Verdana;">p</sup><span style="font-family:Verdana;"> <span style="font-family:Verdana;">to <span style="font-family:Verdana;">H<span style="font-family:Verdana;"><sup><span style="white-space:normal;font-family:Verdana;">2 </sup><span style="font-family:Verdana;">for some 1 <span style="font-family:Verdana;">≤ <span style="font-family:Verdana;">p < <span style="font-family:Verdana;">2, where the range of <span style="font-family:Verdana;">p <span style="font-family:CMR10;"><span style="font-family:Verdana;">is depending on a growth condition. To prove that, we generalize the Hausdorff-Young Theorem to multi-dimensional case.
文摘The weak-type (1, 1) boundedness of the higher order Riesz-Laguerre transforms associated with the Laguerre polynomials and the boundedness for the Riesz-Laguerre transforms of order 2 are considered. We discuss a polynomial weight w that makes the Riesz-Laguerre transforms of order greater than or equal to 2 continuous from L<sup>1</sup> (wdμ<sub>α</sub>) into L<sup>1,∞</sup> (dμ<sub>α</sub>), under specific value α, where μα</sub> is the Laguerre measure.
