A₁-regularity and boundedness of Calderón-Zygmund operators

• Autorzy: Dmitry V. Rutsky
• Języki publikacji: EN

Abstrakty

EN

The Coifman-Fefferman inequality implies quite easily that a Calderón-Zygmund operator T acts boundedly in a Banach lattice X on ℝⁿ if the Hardy-Littlewood maximal operator M is bounded in both X and X'. We establish a converse result under the assumption that X has the Fatou property and X is p-convex and q-concave with some 1 < p, q < ∞: if a linear operator T is bounded in X and T is nondegenerate in a certain sense (for example, if T is a Riesz transform) then M is bounded in both X and X'.

Kategorie tematyczne

• 47B38: Operators on function spaces (general)
• 46E30: Spaces of measurable functions ( L p -spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
• 42B25: Maximal functions, Littlewood-Paley theory
• 42B20: Singular and oscillatory integrals (Calder\'on-Zygmund, etc.)
• 46B42: Banach lattices

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2014
• Tom: 221
• Numer: 3
• Strony: 231-247

Daty

wydano

2014

Twórcy

autor

Dmitry V. Rutsky

• Steklov Mathematical Institute, St. Petersburg Branch, Fontanka 27, 191023 St. Petersburg, Russia

Identyfikatory

DOI

10.4064/sm221-3-3