Displaying similar documents to “Topics in dyadic Dirichlet spaces.”

Norm and Taylor coefficients estimates of holomorphic functions in balls

Jacob Burbeam, Do Young Kwak (1991)

Annales Polonici Mathematici

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A classical result of Hardy and Littlewood states that if f ( z ) = ∑ m = 0 ∞ a m z m is in H p , 0 < p ≤ 2, of the unit disk of ℂ, then ∑ m = 0 ∞ ( m + 1 ) p - 2 | a m | p ≤ c p ∥ f ∥ p p where c p is a positive constant depending only on p. In this paper, we provide an extension of this result to Hardy and weighted Bergman spaces in the unit ball of ℂ n , and use this extension to study some related multiplier problems in ℂ n .

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...

Monotonicity in Banach function spaces

Sinnamon, Gord

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This paper is an informal presentation of material from [28]–[34]. The monotone envelopes of a function, including the level function, are introduced and their properties are studied. Applications to norm inequalities are given. The down space of a Banach function space is defined and connections are made between monotone envelopes and the norms of the down space and its dual. The connection is shown to be particularly close in the case of universally rearrangement invariant spaces....