Boundedness of Operators on Weighted Morrey-Campanato Spaces in the Bessel Setting

Let lambda is an element of(-12,infinity), and{W lambda t}t>0be the heat semigroup related to the BesselSchr & ouml;dinger operatorS lambda:= -d2dx2+lambda 2-lambda x2onR+:=(0,infinity). The authors intro-duce the weighted Morrey-Campanato space BMO alpha(R+,omega)with alpha is an element of[0,1)and omega is an element of A infinity(R+), and show that for any weight function omega is an element of RHs '(R+)boolean AND Ap/s(R+),the oscillation, variation, radial maximal operator, and maximal operator of differenceassociated with the family{tm partial derivative mtW lambda t}t>0are bounded from BMO alpha(R+,omega)to its sub-space BLO alpha(R+,omega), where lambda is an element of R+,m is an element of N boolean OR{0},p is an element of(1,infinity),s is an element of[1,p)such thatp/s+alpha<1+min{1,lambda}, ands ' denotes the conjugate exponent ofs. These resultsare new even in the case of omega equivalent to 1. As a corollary, the boundedness of these operatorson spaces BMO alpha(R+,omega)is further established