Displaying similar documents to “Erratum : Notes on interpolation of Hardy spaces”

Notes on interpolation of Hardy spaces

Quanhua Xu (1992)

Annales de l'institut Fourier

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Let H p denote the usual Hardy space of analytic functions on the unit disc ( 0 < p ) . We prove that for every function f H 1 there exists a linear operator T defined on L 1 ( T ) which is simultaneously bounded from L 1 ( T ) to H 1 and from L ( T ) to H such that T ( f ) = f . Consequently, we get the following results ( 1 p 0 , p 1 ) : 1) ( H p 0 , H p 1 ) is a Calderon-Mitjagin couple; 2) for any interpolation functor F , we have F ( H p 0 , H p 1 ) = H ( F ( L p 0 ( T ) , L p 1 ( T ) ) ) , where H ( F ( L p 0 ( T ) , L p 1 ( T ) ) ) denotes the closed subspace of F ( L p 0 ( T ) , L p 1 ( T ) ) of all functions whose Fourier coefficients...

On interpolation error on degenerating prismatic elements

Ali Khademi, Sergey Korotov, Jon Eivind Vatne (2018)

Applications of Mathematics

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We propose an analogue of the maximum angle condition (commonly used in finite element analysis for triangular and tetrahedral meshes) for the case of prismatic elements. Under this condition, prisms in the meshes may degenerate in certain ways, violating the so-called inscribed ball condition presented by P. G. Ciarlet (1978), but the interpolation error remains of the order O ( h ) in the H 1 -norm for sufficiently smooth functions.

The Hardy-Lorentz spaces H p , q ( )

Wael Abu-Shammala, Alberto Torchinsky (2007)

Studia Mathematica

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We deal with the Hardy-Lorentz spaces H p , q ( ) where 0 < p ≤ 1, 0 < q ≤ ∞. We discuss the atomic decomposition of the elements in these spaces, their interpolation properties, and the behavior of singular integrals and other operators acting on them.

A note on rearrangements of Fourier coefficients

Hugh L. Montgomery (1976)

Annales de l'institut Fourier

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Let f ( x ) Σ a n e 2 π i n x , f * ( x ) n = 0 a * n cos 2 π n x , where the a * n are the numbers | a n | rearranged so that a n * 0 . Then for any convex increasing ψ , ψ ( | f | 2 1 ψ ( 20 | f * | 2 1 . The special case ψ ( t ) = t q / 2 , q 2 , gives f q 5 f * q an equivalent of Littlewood.

Anisotropic h p -adaptive method based on interpolation error estimates in the H 1 -seminorm

Vít Dolejší (2015)

Applications of Mathematics

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We develop a new technique which, for the given smooth function, generates the anisotropic triangular grid and the corresponding polynomial approximation degrees based on the minimization of the interpolation error in the broken H 1 -seminorm. This technique can be employed for the numerical solution of boundary value problems with the aid of finite element methods. We present the theoretical background of this approach and show several numerical examples demonstrating the efficiency of...

Harmonic interpolating sequences, L p and BMO

John B. Garnett (1978)

Annales de l'institut Fourier

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Let ( z ν ) be a sequence in the upper half plane. If 1 &lt; p and if y ν 1 / p f ( z ν ) = a ν , ν = 1 , 2 , ... ( * ) has solution f ( z ) in the class of Poisson integrals of L p functions for any sequence ( a ν ) p , then we show that ( z ν ) is an interpolating sequence for H . If f ( z ν ) = a ν , ν = 1 , 2 , ... has solution in the class of Poisson integrals of BMO functions whenever ( a ν ) , then ( z ν ) is again an interpolating sequence for H . A somewhat more general theorem is also proved and a counterexample for the case p 1 is described.

Several notes on the circumradius condition

Václav Kučera (2016)

Applications of Mathematics

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Recently, the so-called circumradius condition (or estimate) was derived, which is a new estimate of the W 1 , p -error of linear Lagrange interpolation on triangles in terms of their circumradius. The published proofs of the estimate are rather technical and do not allow clear, simple insight into the results. In this paper, we give a simple direct proof of the p = case. This allows us to make several observations such as on the optimality of the circumradius estimate. Furthermore, we show how...

Interpolation of Cesàro sequence and function spaces

Sergey V. Astashkin, Lech Maligranda (2013)

Studia Mathematica

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The interpolation properties of Cesàro sequence and function spaces are investigated. It is shown that C e s p ( I ) is an interpolation space between C e s p ( I ) and C e s p ( I ) for 1 < p₀ < p₁ ≤ ∞ and 1/p = (1 - θ)/p₀ + θ/p₁ with 0 < θ < 1, where I = [0,∞) or [0,1]. The same result is true for Cesàro sequence spaces. On the other hand, C e s p [ 0 , 1 ] is not an interpolation space between Ces₁[0,1] and C e s [ 0 , 1 ] .