A transplantation theorem for ultraspherical polynomials at critical index

• Autorzy: J. J. Guadalupe , V. I. Kolyada
• Języki publikacji: EN

Abstrakty

EN

We investigate the behaviour of Fourier coefficients with respect to the system of ultraspherical polynomials. This leads us to the study of the "boundary" Lorentz space $ℒ_{λ}$ corresponding to the left endpoint of the mean convergence interval. The ultraspherical coefficients ${cₙ^{(λ)}(f)}$ of $ℒ_{λ}$-functions turn out to behave like the Fourier coefficients of functions in the real Hardy space ReH¹. Namely, we prove that for any $f ∈ ℒ_{λ}$ the series $∑_{n=1}^{∞} cₙ^{(λ)}(f) cos nθ $ is the Fourier series of some function φ ∈ ReH¹ with $||φ||_{ReH¹} ≤ c||f||_{ℒ_{λ}}$.

Kategorie tematyczne

• 33C45: Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
• 42A50: Conjugate functions, conjugate series, singular integrals
• 42C10: Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2001
• Tom: 147
• Numer: 1
• Strony: 51-72

Daty

wydano

2001

Twórcy

autor

J. J. Guadalupe

• Departamento de Matemáticas y Computación, Universidad de La Rioja, Edif. Vives, c. Luis de Ulloa, 26004 Logroño, La Rioja, Spain

autor

V. I. Kolyada

• Department of Mathematics, Odessa National University, 2 Dvoryanskaya st., 270000 Odessa, Ukraine

Identyfikatory

DOI

10.4064/sm147-1-5