In this paper, we establish sufficient conditions on weights which ensurethat high-order Riesz-Bessel transformations generated by the generalized shift operator actboundedly from one weighted L_p-space into another.
A necessary and sufficient condition for the generalized shift operator T=S-k-(a(1)((1)),a(2)((1)),...)x e(1)-...-(a(1)((j)),a(2)((j)),...)x e(j)(j greater than or equal to k)on l(1)to be power bounded is obtained.Mor...A necessary and sufficient condition for the generalized shift operator T=S-k-(a(1)((1)),a(2)((1)),...)x e(1)-...-(a(1)((j)),a(2)((j)),...)x e(j)(j greater than or equal to k)on l(1)to be power bounded is obtained.Moreover,this note points out that the power bounded operator T=S-(1,1,...)x c(1)can shift a basis of[e(j+1)-e(j)](j=1)(infinity),and this basis is not equivalent to{T(n)e(1)}(infinity)(n=0).展开更多
文摘In this paper, we establish sufficient conditions on weights which ensurethat high-order Riesz-Bessel transformations generated by the generalized shift operator actboundedly from one weighted L_p-space into another.
基金the Education Department Foundation of Henan province.
文摘A necessary and sufficient condition for the generalized shift operator T=S-k-(a(1)((1)),a(2)((1)),...)x e(1)-...-(a(1)((j)),a(2)((j)),...)x e(j)(j greater than or equal to k)on l(1)to be power bounded is obtained.Moreover,this note points out that the power bounded operator T=S-(1,1,...)x c(1)can shift a basis of[e(j+1)-e(j)](j=1)(infinity),and this basis is not equivalent to{T(n)e(1)}(infinity)(n=0).
