# 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 (2007)

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

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topMichael 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

top- [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] M. Felten: “Most of the First Order Jacobi K-Functionals are Equivalent”, submitted, pp. 1–12.
- [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] B. Muckenhoupt: “Transplantation theorems and multiplier theorems for Jacobi series”, Mem. Amer. Math. Soc., Vol. 64, (1986), pp. iv–86. Zbl0611.42020