Displaying similar documents to “ H 1 -BMO duality on graphs”

On some structural properties of Banach function spaces and boundedness of certain integral operators

T. S. Kopaliani (2004)

Czechoslovak Mathematical Journal

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In this paper the notions of uniformly upper and uniformly lower ℓ -estimates for Banach function spaces are introduced. Further, the pair ( X , Y ) of Banach function spaces is characterized, where X and Y satisfy uniformly a lower ℓ -estimate and uniformly an upper ℓ -estimate, respectively. The integral operator from X into Y of the form K f ( x ) = ϕ ( x ) ∫ 0 x k ( x , y ) f ( y ) ψ ( y ) d y is studied, where k , ϕ , ψ are prescribed functions under some local integrability conditions, the kernel k is non-negative and is assumed to satisfy certain...

Commutators of singular integrals on spaces of homogeneous type

Gladis Pradolini, Oscar Salinas (2007)

Czechoslovak Mathematical Journal

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In this work we prove some sharp weighted inequalities on spaces of homogeneous type for the higher order commutators of singular integrals introduced by R. Coifman, R. Rochberg and G. Weiss in Factorization theorems for Hardy spaces in several variables, Ann. Math. 103 (1976), 611–635. As a corollary, we obtain that these operators are bounded on L p ( w ) when w belongs to the Muckenhoupt’s class A p , p > 1 . In addition, as an important tool in order to get our main result, we prove a weighted Fefferman-Stein...

Linear elliptic equations with BMO coefficients

Menita Carozza, Gioconda Moscariello, Antonia Passarelli di Napoli (1999)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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We prove an existence and uniqueness theorem for the Dirichlet problem for the equation div ⁢ a ⁢ x ⁢ ∇ ⁡ u = div ⁢ f in an open cube Ω ⊂ R N , when f belongs to some L p ⁢ Ω , with p close to 2. Here we assume that the coefficient a belongs to the space BMO( Ω ) of functions of bounded mean oscillation and verifies the condition a ⁢ x ≥ λ 0 > 0 for a.e. x ∈ Ω .

The Fourier integral operators on Hardy spaces associated with Herz spaces

Lixia Liu, Bolin Ma, Sanyang Liu (2011)

Czechoslovak Mathematical Journal

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In this paper, it is proved that the Fourier integral operators of order m , with - n < m ≤ - ( n - 1 ) / 2 , are bounded from three kinds of Hardy spaces associated with Herz spaces to their corresponding Herz spaces.