Boundedness of oscillation and variation of semigroups associated with Bessel Schrodinger operators

Let lambda is an element of (- 1/2, infinity) and S-lambda := -d(2)/dx(2) + lambda(2) -lambda/x(2) be the Bessel Schrodinger operator on R+ := (0, infinity). The authors obtain the sharp power-weighted L-p, weak type and restricted weak type inequalities for the oscillation operator O-{ti} i is an element of N ({t(m) partial derivative(m)(t) W-t(lambda)}(t>0), center dot) and the variation operator V-p({t(m) partial derivative(m)(t) W-t(lambda)}(t>0), center dot) of the heat semigroup {W-t(lambda)}(t>0) associated with S-lambda, where p is an element of (2, infinity) and m is an element of Z+ := N. {0}. Moreover, for.. (0,8), the boundedness of O-{ti} i is an element of N ({t(m) partial derivative(m)(t) W-t(lambda)}(t>0), center dot) and V-p({t(m) partial derivative(m)(t) W-t(lambda)}(t>0), center dot) from the Hardy space H-p(R+) into L-p(R+) with p is an element of (1/2, 1] and on the Campanato type spaces BMO alpha(R+) with alpha is an element of [0, 1)boolean AND(0, lambda) are obtained. (C) 2020 Elsevier Ltd. All rights reserved.