Regularity and continuity of commutators of the Hardy–Littlewood maximal function
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DOI: 10.1002/mana.201900013
Abstract: Let M be the Hardy–Littlewood maximal function and let [b,M] be its corresponding commutator. For 1 read more here.
Keywords: hardy littlewood; littlewood maximal; continuity commutators; maximal function ... See more keywords
Schrödinger‐Poisson system with Hardy‐Littlewood‐Sobolev critical exponent
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DOI: 10.1002/mma.5694
Abstract: In this paper, we consider the following Schrödinger‐Poisson system: −Δu+λϕ|u|2α∗−2u=∫R3|u|2β∗|x−y|3−βdy|u|2β∗−2u,inR3,(−Δ)α2ϕ=Aα−1|u|2α∗,inR3, where parameters α,β∈(0,3),λ>0, Aα=Γ(3−α2)2απ32Γ(α2) , 2α∗=3+α , and 2β∗=3+β are the Hardy‐Littlewood‐Sobolev critical exponents. For α0, we prove the existence of nonnegative groundstate solution to… read more here.
Keywords: dinger poisson; system; hardy littlewood; littlewood sobolev ... See more keywords
Sharp Anisotropic Hardy–Littlewood Inequality for Positive Multilinear Forms
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DOI: 10.1007/s00025-019-1120-x
Abstract: Using elementary techniques, we prove sharp anisotropic Hardy-Littlewood inequalities for positive multilinear forms. In particular, we recover an inequality proved by F. Bayart in 2018. read more here.
Keywords: hardy littlewood; anisotropic hardy; positive multilinear; sharp anisotropic ... See more keywords
Hardy—Littlewood—Sobolev Inequalities with the Fractional Poisson Kernel and Their Applications in PDEs
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DOI: 10.1007/s10114-019-8417-2
Abstract: The purpose of this paper is five-fold. First, we employ the harmonic analysis techniques to establish the following Hardy-Littlewood-Sobolev inequality with the fractional Poisson kernel on the upper half space $$\int_{\mathbb{R}_ + ^n} {{{\int_{\partial \mathbb{R}_… read more here.
Keywords: fractional poisson; hardy littlewood; mathbb; littlewood sobolev ... See more keywords
Multiplicity Results for Kirchhoff Equations with Hardy-Littlewood-Sobolev Critical Nonlinearity
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DOI: 10.1007/s10883-019-09456-3
Abstract: In this paper, we deal with the multiplicity results for Kirchhoff equations with Hardy-Littlewood-Sobolev critical nonlinearity in ℝ N $\mathbb {R}^{N}$ . By using the second concentration-compactness principle and concentration-compactness principle at infinity to prove… read more here.
Keywords: equations hardy; hardy littlewood; littlewood sobolev; results kirchhoff ... See more keywords
Some applications of the regularity principle in sequence spaces
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DOI: 10.1007/s11117-017-0506-9
Abstract: The Hardy–Littlewood inequalities for m-linear forms have their origin with the seminal paper of Hardy and Littlewood (Q J Math 5:241–254, 1934). Nowadays it has been extensively investigated and many authors are looking for the… read more here.
Keywords: regularity principle; hardy littlewood; mathbb mathbb; mathbb ... See more keywords
Boundedness of both discrete Hardy and Hardy–Littlewood maximal operators via Muckenhoupt weights
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DOI: 10.1216/rmj.2021.51.733
Abstract: We employ the self-improving property (backward propagation) for the discrete Muckenhoupt class ????p, to prove that both discrete Hardy and discrete Hardy–Littlewood maximal operators are bounded on the usual weighted Lebesgue space lup(ℤ+) if and… read more here.
Keywords: hardy littlewood; hardy; littlewood maximal; maximal operators ... See more keywords
A Hardy–Littlewood theorem for Bergman spaces
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DOI: 10.5186/aasfm.2018.4345
Abstract: Let D be the open unit disk in the complex plane C and let H(D) denote the space of all analytic functions on D. For p > 0 and α > −1 we consider the… read more here.
Keywords: hardy littlewood; theorem bergman; bergman spaces; littlewood theorem ... See more keywords