TY - JOUR

T1 - Fractional integration of summable functions: Maz'ya's Φ-inequalities

AU - Stolyarov, D.

N1 - Export Date: 27 October 2024 Сведения о финансировании: Russian Science Foundation, RSF, N 19-71-10023 Текст о финансировании 1: Supported by the Russian Science Foundation grant N 19-71-10023. Received September 27, 2021; accepted in revised form January 23, 2023. Published online September 2024.

PY - 2023/3/7

Y1 - 2023/3/7

N2 - We study inequalities of the type j R Rd Φ(K*f )| ≲ ∥f ∥p L1(Rd ) , where the kernel K is homogeneous of order α - d and possibly vector-valued, the function Φ is positively p-homogeneous, and p = d/(d - α). Under mild regularity assumptions on K and Φ, we find necessary and sufficient conditions on these functions under which the inequality holds true with a uniform constant for all sufficiently regular functions f . © 2024 Scuola Normale Superiore. All rights reserved.

AB - We study inequalities of the type j R Rd Φ(K*f )| ≲ ∥f ∥p L1(Rd ) , where the kernel K is homogeneous of order α - d and possibly vector-valued, the function Φ is positively p-homogeneous, and p = d/(d - α). Under mild regularity assumptions on K and Φ, we find necessary and sufficient conditions on these functions under which the inequality holds true with a uniform constant for all sufficiently regular functions f . © 2024 Scuola Normale Superiore. All rights reserved.

UR - https://www.mendeley.com/catalogue/341064c7-b39b-3e15-aba9-089adf94fa23/

U2 - 10.2422/2036-2145.202110_001

DO - 10.2422/2036-2145.202110_001

M3 - статья

VL - 25

SP - 1727

EP - 1752

JO - Annali della Scuola normale superiore di Pisa - Classe di scienze

JF - Annali della Scuola normale superiore di Pisa - Classe di scienze

SN - 0391-173X

IS - 3

ER -