Littlewood-Paley theory for variable exponent Lebesgue spaces and Gagliardo-Nirenberg inequality for Riesz potentials

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Abstract

Our aim in this paper is to prove the Gagliardo-Nirenberg inequality for Riesz potentials of functions in variable exponent Lebesgue spaces, which are called Musielak-Orlicz spaces with respect to Φ(<i>x,t</i>) = <i>t</i><sup><i>p</i>(<i>x</i>)</sup>(log(<i>c</i><sub>0</sub> + <i>t</i>))<sup><i>q</i>(<i>x</i>)</sup> for <i>t</i> > 0 and <i>x</i> ∈ ℝ<sup><i>n</i></sup>, via the Littlewood-Paley decomposition.

Journal

  • Journal of the Mathematical Society of Japan

    Journal of the Mathematical Society of Japan 65(2), 633-670, 2013-04-01

    The Mathematical Society of Japan

References:  46

Codes

  • NII Article ID (NAID)
    10031177293
  • NII NACSIS-CAT ID (NCID)
    AA0070177X
  • Text Lang
    ENG
  • Article Type
    ART
  • ISSN
    00255645
  • NDL Article ID
    024429226
  • NDL Call No.
    Z53-A209
  • Data Source
    CJP  NDL  J-STAGE 
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