Under which conditions is the Jacobi space L w ( a , b ) p [ - 1 , 1 ] subset of L w ( α , β ) 1 [ - 1 , 1 ] ?

Michael Felten

Open Mathematics (2007)

  • Volume: 5, Issue: 3, page 505-511
  • ISSN: 2391-5455

Abstract

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Exact conditions for α, β, a, b > −1 and 1 ≤ p ≤ ∞ are determined under which the inclusion property L w ( a , b ) p [ - 1 , 1 ] ⊂ L w ( α , β ) 1 [ - 1 , 1 ] is valid. It is shown that the conditions characterize the inclusion property. The paper concludes with some results, in which the inclusion property can be detected in relation with estimates of Jacobi differential operators and with Muckenhoupt’s transplantation theorems and multiplier theorems for Jacobi series.

How to cite

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Michael Felten. "Under which conditions is the Jacobi space \[L_{w^{(a,b)} }^p [ - 1,1]\] subset of \[L_{w^{(\alpha ,\beta )} }^1 [ - 1,1]\] ?." Open Mathematics 5.3 (2007): 505-511. <http://eudml.org/doc/269527>.

@article{MichaelFelten2007,
abstract = {Exact conditions for α, β, a, b > −1 and 1 ≤ p ≤ ∞ are determined under which the inclusion property \[L\_\{w^\{(a,b)\} \}^p [ - 1,1]\] ⊂ \[L\_\{w^\{(\alpha ,\beta )\} \}^1 [ - 1,1]\] is valid. It is shown that the conditions characterize the inclusion property. The paper concludes with some results, in which the inclusion property can be detected in relation with estimates of Jacobi differential operators and with Muckenhoupt’s transplantation theorems and multiplier theorems for Jacobi series.},
author = {Michael Felten},
journal = {Open Mathematics},
keywords = {Jacobi Spaces; Fourier expansion; Jacobi differential operators; transplantation theorems; multiplier theorems},
language = {eng},
number = {3},
pages = {505-511},
title = {Under which conditions is the Jacobi space \[L\_\{w^\{(a,b)\} \}^p [ - 1,1]\] subset of \[L\_\{w^\{(\alpha ,\beta )\} \}^1 [ - 1,1]\] ?},
url = {http://eudml.org/doc/269527},
volume = {5},
year = {2007},
}

TY - JOUR
AU - Michael Felten
TI - Under which conditions is the Jacobi space \[L_{w^{(a,b)} }^p [ - 1,1]\] subset of \[L_{w^{(\alpha ,\beta )} }^1 [ - 1,1]\] ?
JO - Open Mathematics
PY - 2007
VL - 5
IS - 3
SP - 505
EP - 511
AB - Exact conditions for α, β, a, b > −1 and 1 ≤ p ≤ ∞ are determined under which the inclusion property \[L_{w^{(a,b)} }^p [ - 1,1]\] ⊂ \[L_{w^{(\alpha ,\beta )} }^1 [ - 1,1]\] is valid. It is shown that the conditions characterize the inclusion property. The paper concludes with some results, in which the inclusion property can be detected in relation with estimates of Jacobi differential operators and with Muckenhoupt’s transplantation theorems and multiplier theorems for Jacobi series.
LA - eng
KW - Jacobi Spaces; Fourier expansion; Jacobi differential operators; transplantation theorems; multiplier theorems
UR - http://eudml.org/doc/269527
ER -

References

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  1. [1] F. Dai and Z. Ditzian: “Littlewood-Paley theory and a sharp Marchaud inequality”, Acta Sci. Math. (Szeged), Vol. 71, (2005), pp. 65–90. Zbl1101.26007
  2. [2] M. Felten: “Most of the First Order Jacobi K-Functionals are Equivalent”, submitted, pp. 1–12. 
  3. [3] B. Muckenhoupt: “Mean convergence of Jacobi series”, Proc. Amer. Math. Soc., Vol. 23, (1969), pp. 306–310. http://dx.doi.org/10.2307/2037162 Zbl0182.39701
  4. [4] B. Muckenhoupt: “Transplantation theorems and multiplier theorems for Jacobi series”, Mem. Amer. Math. Soc., Vol. 64, (1986), pp. iv–86. Zbl0611.42020

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