One-weight weak type estimates for fractional and singular integrals in grand Lebesgue spaces

• Autorzy: Vakhtang Kokilashvili , Alexander Meskhi
• Języki publikacji: EN

Abstrakty

EN

We investigate weak type estimates for maximal functions, fractional and singular integrals in grand Lebesgue spaces. In particular, we show that for the one-weight weak type inequality it is necessary and sufficient that a weight function belongs to the appropriate Muckenhoupt class. The same problem is discussed for strong maximal functions, potentials and singular integrals with product kernels.

Kategorie tematyczne

• 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.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2014
• Tom: 102
• Numer: 1
• Strony: 131-142

Daty

wydano

2014

Twórcy

autor

Vakhtang Kokilashvili

• Department of Mathematical Analysis, A. Razmadze Mathematical Institute, I. Javakhishvili Tbilisi State University, 2 University St., Tbilisi 0186
• International Black Sea University, 3 Agmashenebeli Ave., Tbilisi 0131, Georgia

autor

Alexander Meskhi

• Department of Mathematical Analysis, A. Razmadze Mathematical Institute, I. Javakhishvili Tbilisi State University, 2 University St., Tbilisi 0186, Georgia
• Department of Mathematics, Faculty of Informatics and Control Systems, Georgian Technical University, 77 Kostava St., Tbilisi 0175, Georgia

Identyfikatory

DOI

10.4064/bc102-0-9