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Fractional Gagliardo–Nirenberg interpolation inequality and bounded mean oscillation
Comptes Rendus. Mathématique, 2023 We prove Gagliardo–Nirenberg interpolation inequalities estimating the Sobolev semi-norm in terms of the bounded mean oscillation semi-norm and of a Sobolev semi-norm, with some of the Sobolev semi-norms having fractional order.
Van Schaftingen, Jean
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Mean oscillation bounds on rearrangements [PDF]
Transactions of the American Mathematical Society, 2022 We use geometric arguments to prove explicit bounds on the mean oscillation for two important rearrangements on R n {\mathbb {R}^n} . For the decreasing rearrangement f ∗ f^* of a rearrangeable function f f of bounded mean ...
Burchard, Almut +2 more
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Fractional operators and their commutators on generalized Orlicz spaces [PDF]
Opuscula Mathematica, 2022 In this paper we examine boundedness of fractional maximal operator. The main focus is on commutators and maximal commutators on generalized Orlicz spaces (also known as Musielak-Orlicz spaces) for fractional maximal functions and Riesz potentials.
Arttu Karppinen
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Hydrodynamic normalization conditions in the theory of degenerate Beltrami equations
Доповiдi Нацiональної академiї наук України, 2023 We study the existence of normalized homeomorphic solutions for the degenerate Beltrami equation fz = μ(z )f in the whole complex plane C , assuming that its measurable coefficient μ(z ), | μ(z ) |
V.Ya. Gutlyanskiĭ +3 more
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FUNCTIONS OF BOUNDED MEAN OSCILLATION [PDF]
Taiwanese Journal of Mathematics, 2006 $BMO$, the space of functions of bounded mean oscillation, was first introduced by F. John and L. Nirenberg in 1961. It became a focus of attention when C. Fefferman proved that $BMO$ is the dual of the (real) Hardy space $H^1$ in 1971. In the past 30 years, this space was studied extensively by many mathematicians.
Chang, Der-Chen, Sadosky, Cora
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Variable λ-Central Morrey Space Estimates for the Fractional Hardy Operators and Commutators
Journal of Mathematics, 2022 This paper aims to show that the fractional Hardy operator and its adjoint operator are bounded on central Morrey space with variable exponent. Similar results for their commutators are obtained when the symbol functions belong to λ-central bounded mean ...
Amjad Hussain, Muhammad Asim, Fahd Jarad
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Journal of Function Spaces, 2022 In this paper, we establish the boundedness of the modified fractional integral operator from mixed Morrey spaces to the bounded mean oscillation space and Lipschitz spaces, respectively.
Mingquan Wei, Lanyin Sun
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On the Dirichlet problem for de ge nerate Beltrami equations
Доповiдi Нацiональної академiї наук України, 2023 We study the Dirichlet problem as with continuous boundary data in arbitrary simply connected bounded domains D of the complex plane where f satisfies the degenerate Beltrami equation a. e. in D.
V.Ya. Gutlyanskiĭ +3 more
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WEIGHTED VARIABLE HARDY SPACES ASSOCIATED WITH OPERATORS SATISFYING DAVIES-GAFFNEY ESTIMATES
Проблемы анализа, 2022 We introduce the weighted variable Hardy space 𝐻(^𝑝(·) _𝐿,𝑤) (ℝ^𝑛) associated with the operator 𝐿, which has a bounded holomorphic functional calculus and fulfills the Davies-Gaffney estimates. More precisely, we establish the molecular characterization
B. Laadjal +3 more
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An improvement to the John-Nirenberg inequality for functions in critical Sobolev spaces
Advances in Nonlinear Analysis, 2020 It is known that functions in a Sobolev space with critical exponent embed into the space of functions of bounded mean oscillation, and therefore satisfy the John-Nirenberg inequality and a corresponding exponential integrability estimate.
Martínez Ángel D., Spector Daniel
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