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

• Víctor Almeida ^[1] ; Betancor, Jorge J. ^[1] ; Fariña, Juan C. ^[1] ; Lourdes Rodríguez-Mesa ^[1]
  1. [1] Universidad de La Laguna

     Universidad de La Laguna

     San Cristóbal de La Laguna, España

     
• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 66, Nº. 1, 2023, págs. 1-34
• Idioma: inglés
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• Resumen

  • 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.