Let λ∈(-12,∞){Wtλ}t>0Sλ:=-d2dx2+λ2-λx2R+:=(0,∞)BMOα(R+,ω)α∈[0,1)ω∈A∞(R+)ω∈RHs′(R+)∩Ap/s(R+){tm∂tmWtλ}t>0BMOα(R+,ω)BLOα(R+,ω)λ∈R+m∈N∪{0}p∈(1,∞)s∈[1,p)p/s+α<1+min{1,λ}s′ω≡1BMOα(R+,ω), and λ∈(-12,∞){Wtλ}t>0Sλ:=-d2dx2+λ2-λx2R+:=(0,∞)BMOα(R+,ω)α∈[0,1)ω∈A∞(R+)ω∈RHs′(R+)∩Ap/s(R+){tm∂tmWtλ}t>0BMOα(R+,ω)BLOα(R+,ω)λ∈R+m∈N∪{0}p∈(1,∞)s∈[1,p)p/s+α<1+min{1,λ}s′ω≡1BMOα(R+,ω) be the heat semigroup related to the Bessel Schrödinger operator λ∈(-12,∞){Wtλ}t>0Sλ:=-d2dx2+λ2-λx2R+:=(0,∞)BMOα(R+,ω)α∈[0,1)ω∈A∞(R+)ω∈RHs′(R+)∩Ap/s(R+){tm∂tmWtλ}t>0BMOα(R+,ω)BLOα(R+,ω)λ∈R+m∈N∪{0}p∈(1,∞)s∈[1,p)p/s+α<1+min{1,λ}s′ω≡1BMOα(R+,ω) on λ∈(-12,∞){Wtλ}t>0Sλ:=-d2dx2+λ2-λx2R+:=(0,∞)BMOα(R+,ω)α∈[0,1)ω∈A∞(R+)ω∈RHs′(R+)∩Ap/s(R+){tm∂tmWtλ}t>0BMOα(R+,ω)BLOα(R+,ω)λ∈R+m∈N∪{0}p∈(1,∞)s∈[1,p)p/s+α<1+min{1,λ}s′ω≡1BMOα(R+,ω). The authors introduce the weighted Morrey–Campanato space λ∈(-12,∞){Wtλ}t>0Sλ:=-d2dx2+λ2-λx2R+:=(0,∞)BMOα(R+,ω)α∈[0,1)ω∈A∞(R+)ω∈RHs′(R+)∩Ap/s(R+){tm∂tmWtλ}t>0BMOα(R+,ω)BLOα(R+,ω)λ∈R+m∈N∪{0}p∈(1,∞)s∈[1,p)p/s+α<1+min{1,λ}s′ω≡1BMOα(R+,ω) with λ∈(-12,∞){Wtλ}t>0Sλ:=-d2dx2+λ2-λx2R+:=(0,∞)BMOα(R+,ω)α∈[0,1)ω∈A∞(R+)ω∈RHs′(R+)∩Ap/s(R+){tm∂tmWtλ}t>0BMOα(R+,ω)BLOα(R+,ω)λ∈R+m∈N∪{0}p∈(1,∞)s∈[1,p)p/s+α<1+min{1,λ}s′ω≡1BMOα(R+,ω) and λ∈(-12,∞){Wtλ}t>0Sλ:=-d2dx2+λ2-λx2R+:=(0,∞)BMOα(R+,ω)α∈[0,1)ω∈A∞(R+)ω∈RHs′(R+)∩Ap/s(R+){tm∂tmWtλ}t>0BMOα(R+,ω)BLOα(R+,ω)λ∈R+m∈N∪{0}p∈(1,∞)s∈[1,p)p/s+α<1+min{1,λ}s′ω≡1BMOα(R+,ω), and show that for any weight function λ∈(-12,∞){Wtλ}t>0Sλ:=-d2dx2+λ2-λx2R+:=(0,∞)BMOα(R+,ω)α∈[0,1)ω∈A∞(R+)ω∈RHs′(R+)∩Ap/s(R+){tm∂tmWtλ}t>0BMOα(R+,ω)BLOα(R+,ω)λ∈R+m∈N∪{0}p∈(1,∞)s∈[1,p)p/s+α<1+min{1,λ}s′ω≡1BMOα(R+,ω), the oscillation, variation, radial maximal operator, and maximal operator of difference associated with the family λ∈(-12,∞){Wtλ}t>0Sλ:=-d2dx2+λ2-λx2R+:=(0,∞)BMOα(R+,ω)α∈[0,1)ω∈A∞(R+)ω∈RHs′(R+)∩Ap/s(R+){tm∂tmWtλ}t>0BMOα(R+,ω)BLOα(R+,ω)λ∈R+m∈N∪{0}p∈(1,∞)s∈[1,p)p/s+α<1+min{1,λ}s′ω≡1BMOα(R+,ω) are bounded from λ∈(-12,∞){Wtλ}t>0Sλ:=-d2dx2+λ2-λx2R+:=(0,∞)BMOα(R+,ω)α∈[0,1)ω∈A∞(R+)ω∈RHs′(R+)∩Ap/s(R+){tm∂tmWtλ}t>0BMOα(R+,ω)BLOα(R+,ω)λ∈R+m∈N∪{0}p∈(1,∞)s∈[1,p)p/s+α<1+min{1,λ}s′ω≡1BMOα(R+,ω) to its subspace λ∈(-12,∞){Wtλ}t>0Sλ:=-d2dx2+λ2-λx2R+:=(0,∞)BMOα(R+,ω)α∈[0,1)ω∈A∞(R+)ω∈RHs′(R+)∩Ap/s(R+){tm∂tmWtλ}t>0BMOα(R+,ω)BLOα(R+,ω)λ∈R+m∈N∪{0}p∈(1,∞)s∈[1,p)p/s+α<1+min{1,λ}s′ω≡1BMOα(R+,ω), where λ∈(-12,∞){Wtλ}t>0Sλ:=-d2dx2+λ2-λx2R+:=(0,∞)BMOα(R+,ω)α∈[0,1)ω∈A∞(R+)ω∈RHs′(R+)∩Ap/s(R+){tm∂tmWtλ}t>0BMOα(R+,ω)BLOα(R+,ω)λ∈R+m∈N∪{0}p∈(1,∞)s∈[1,p)p/s+α<1+min{1,λ}s′ω≡1BMOα(R+,ω), λ∈(-12,∞){Wtλ}t>0Sλ:=-d2dx2+λ2-λx2R+:=(0,∞)BMOα(R+,ω)α∈[0,1)ω∈A∞(R+)ω∈RHs′(R+)∩Ap/s(R+){tm∂tmWtλ}t>0BMOα(R+,ω)BLOα(R+,ω)λ∈R+m∈N∪{0}p∈(1,∞)s∈[1,p)p/s+α<1+min{1,λ}s′ω≡1BMOα(R+,ω), λ∈(-12,∞){Wtλ}t>0Sλ:=-d2dx2+λ2-λx2R+:=(0,∞)BMOα(R+,ω)α∈[0,1)ω∈A∞(R+)ω∈RHs′(R+)∩Ap/s(R+){tm∂tmWtλ}t>0BMOα(R+,ω)BLOα(R+,ω)λ∈R+m∈N∪{0}p∈(1,∞)s∈[1,p)p/s+α<1+min{1,λ}s′ω≡1BMOα(R+,ω), λ∈(-12,∞){Wtλ}t>0Sλ:=-d2dx2+λ2-λx2R+:=(0,∞)BMOα(R+,ω)α∈[0,1)ω∈A∞(R+)ω∈RHs′(R+)∩Ap/s(R+){tm∂tmWtλ}t>0BMOα(R+,ω)BLOα(R+,ω)λ∈R+m∈N∪{0}p∈(1,∞)s∈[1,p)p/s+α<1+min{1,λ}s′ω≡1BMOα(R+,ω) such that λ∈(-12,∞){Wtλ}t>0Sλ:=-d2dx2+λ2-λx2R+:=(0,∞)BMOα(R+,ω)α∈[0,1)ω∈A∞(R+)ω∈RHs′(R+)∩Ap/s(R+){tm∂tmWtλ}t>0BMOα(R+,ω)BLOα(R+,ω)λ∈R+m∈N∪{0}p∈(1,∞)s∈[1,p)p/s+α<1+min{1,λ}s′ω≡1BMOα(R+,ω), and λ∈(-12,∞){Wtλ}t>0Sλ:=-d2dx2+λ2-λx2R+:=(0,∞)BMOα(R+,ω)α∈[0,1)ω∈A∞(R+)ω∈RHs′(R+)∩Ap/s(R+){tm∂tmWtλ}t>0BMOα(R+,ω)BLOα(R+,ω)λ∈R+m∈N∪{0}p∈(1,∞)s∈[1,p)p/s+α<1+min{1,λ}s′ω≡1BMOα(R+,ω) denotes the conjugate exponent of s. These results are new even in the case of λ∈(-12,∞){Wtλ}t>0Sλ:=-d2dx2+λ2-λx2R+:=(0,∞)BMOα(R+,ω)α∈[0,1)ω∈A∞(R+)ω∈RHs′(R+)∩Ap/s(R+){tm∂tmWtλ}t>0BMOα(R+,ω)BLOα(R+,ω)λ∈R+m∈N∪{0}p∈(1,∞)s∈[1,p)p/s+α<1+min{1,λ}s′ω≡1BMOα(R+,ω). As a corollary, the boundedness of these operators on spaces λ∈(-12,∞){Wtλ}t>0Sλ:=-d2dx2+λ2-λx2R+:=(0,∞)BMOα(R+,ω)α∈[0,1)ω∈A∞(R+)ω∈RHs′(R+)∩Ap/s(R+){tm∂tmWtλ}t>0BMOα(R+,ω)BLOα(R+,ω)λ∈R+m∈N∪{0}p∈(1,∞)s∈[1,p)p/s+α<1+min{1,λ}s′ω≡1BMOα(R+,ω) is further established.