Resumen de Variation and oscillation operators on weighted Morrey–Campanato spaces in the Schrödinger setting

Víctor M. Almeida Lozano, Jorge Juan Betancor Pérez , Juan Carlos Fariña Gil , Lourdes Rodríguez Mesa

• We denote by L the Schr¨odinger operator with potential V , that is, L = −∆ + V , where it is assumed that V satisfies a reverse H¨older inequality. We consider weighted Morrey–Campanato spaces BMOα L,w(Rd) and BLOα L,w(Rd) in the Schr¨odinger setting. We prove that the variation operator Vσ({Tt}t>0), σ > 2, and the oscillation operator O({Tt}t>0, {tj}j∈Z), where tj < tj+1, j ∈ Z, lim j→+∞tj = +∞ and lim j→−∞ tj = 0, being Tt = t k∂ k t e−tL, t > 0, with k ∈ N, are bounded operators from BMOα L,w(Rd) into BLOα L,w(Rd). We also establish the same property for the maximal operators defined by {t k∂ k t e−tL}t>0, k ∈ N.