# Decomposition and Moser's lemma.

David E. Edmunds; Miroslav Krbec

Revista Matemática Complutense (2002)

- Volume: 15, Issue: 1, page 57-74
- ISSN: 1139-1138

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topEdmunds, David E., and Krbec, Miroslav. "Decomposition and Moser's lemma.." Revista Matemática Complutense 15.1 (2002): 57-74. <http://eudml.org/doc/44425>.

@article{Edmunds2002,

abstract = {Using the idea of the optimal decomposition developed in recent papers (Edmunds-Krbec, 2000) and in Cruz-Uribe-Krbec we study the boundedness of the operator Tg(x) = ∫x1 g(u)du / u, x ∈ (0,1), and its logarithmic variant between Lorentz spaces and exponential Orlicz and Lorentz-Orlicz spaces. These operators are naturally linked with Moser's lemma, O'Neil's convolution inequality, and estimates for functions with prescribed rearrangement. We give sufficient conditions for and very simple proofs of uniform boundedness of exponential and double exponential integrals in the spirit of the celebrated lemma due to Moser.},

author = {Edmunds, David E., Krbec, Miroslav},

journal = {Revista Matemática Complutense},

keywords = {Espacio de Orlicz; Espacios de Lorentz; Espacios de Lebesgue; Operadores integrales; Acotación uniforme; function spaces; Lorentz spaces; Moser lemma},

language = {eng},

number = {1},

pages = {57-74},

title = {Decomposition and Moser's lemma.},

url = {http://eudml.org/doc/44425},

volume = {15},

year = {2002},

}

TY - JOUR

AU - Edmunds, David E.

AU - Krbec, Miroslav

TI - Decomposition and Moser's lemma.

JO - Revista Matemática Complutense

PY - 2002

VL - 15

IS - 1

SP - 57

EP - 74

AB - Using the idea of the optimal decomposition developed in recent papers (Edmunds-Krbec, 2000) and in Cruz-Uribe-Krbec we study the boundedness of the operator Tg(x) = ∫x1 g(u)du / u, x ∈ (0,1), and its logarithmic variant between Lorentz spaces and exponential Orlicz and Lorentz-Orlicz spaces. These operators are naturally linked with Moser's lemma, O'Neil's convolution inequality, and estimates for functions with prescribed rearrangement. We give sufficient conditions for and very simple proofs of uniform boundedness of exponential and double exponential integrals in the spirit of the celebrated lemma due to Moser.

LA - eng

KW - Espacio de Orlicz; Espacios de Lorentz; Espacios de Lebesgue; Operadores integrales; Acotación uniforme; function spaces; Lorentz spaces; Moser lemma

UR - http://eudml.org/doc/44425

ER -

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