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2004•Journal of Tongji UniversityRequires access

Interpolation of L_p(M) Spaces

Jing Han

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Abstract

The interpolation properties of a class of Orlicz spaces—L p(M) spaces which are generated by some N-functions that increases faster than power functions are studied in this paper.And the interpolation theorems of linear operators in L p(M) spaces are found.Under some conditions,that the trio (L ∞,L p 0,L p(M)) is an interpolation trio with respect to (L ∞,L p 0,L p()) of exponent θ is also proved.This generalized the known result about the interpolation theorem of linear operators in L p(M) spaces and the classical Lebesgue spaces.

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The interpolation properties of a class of Orlicz spaces—L p(M) spaces which are generated by some N-functions that increases faster than power functions are studied in this paper.And the interpolation theorems of linear operators in L p(M) spaces are found.Under some conditions,that the trio (L ∞,L p 0,L p(M)) is an interpolation trio with respect to (L ∞,L p 0,L p()) of exponent θ is also proved.This generalized the known result about the interpolation theorem of linear operators in L p(M) spaces and the classical Lebesgue spaces.

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Available abstract

The interpolation properties of a class of Orlicz spaces—L p(M) spaces which are generated by some N-functions that increases faster than power functions are studied in this paper.And the interpolation theorems of linear operators in L p(M) spaces are found.Under some conditions,that the trio (L ∞,L p 0,L p(M)) is an interpolation trio with respect to (L ∞,L p 0,L p()) of exponent θ is also proved.This generalized the known result about the interpolation theorem of linear operators in L p(M) spaces and the classical Lebesgue spaces.

Key concepts: Mathematics, Lp space, Interpolation space, Interpolation (computer graphics), Class (philosophy), Linear interpolation, Bilinear interpolation, Pure mathematics

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