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  1. Ana Sayfa
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Yazar "Mamedov, Farman I." seçeneğine göre listele

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  • [ X ]
    Öğe
    On a general weighted Hardy type inequality in the variable exponent Lebesgue spaces
    (Springer-Verlag Italia Srl, 2012) Cruz-Uribe, David; Mamedov, Farman I.
    We study the Hardy type, two-weight inequality for the multidimensional Hardy operator in the variable exponent Lebesgue space L (p(.))(R-n ). We prove equivalent conditions for L-p(.) -> L-q(.) boundness of the Hardy operator in the case of so called mixed exponents: q(0) >= p(0), q(infinity) < p (infinity) or q(0) < p(0), q(infinity) >= p(infinity). We show that a necessary and sufficient condition for such an inequality to hold coincides with conditions for the validity of two weight Hardy inequalities with constant exponents, provided that the exponents are regular at zero and at infinity.
  • [ X ]
    Öğe
    On a Hardy Type General Weighted Inequality in Spaces Lp(.)
    (Springer Basel Ag, 2010) Mamedov, Farman I.; Harman, Aziz
    A Hardy type two-weighted inequality is investigated for the multidimensional Hardy operator in the norms of generalized Lebesgue spaces L-p(.). Equivalent necessary and sufficient conditions are found for the L-p(.) -> L-q(.) boundedness of the Hardy operator when exponents q(0) < p(0), q(infinity) < p(infinity). It is proved that the condition for such an inequality to hold coincides with the condition for the validity of two-weighted Hardy inequalities with constant exponents if we require of the exponents to be regular near zero and at infinity.
  • [ X ]
    Öğe
    On a two-weighted estimation of maximal operator in the Lebesgue space with variable exponent
    (Springer Heidelberg, 2011) Mamedov, Farman I.; Zeren, Yusuf
    We study two-weight inequalities with general-type weights for Hardy-Littlewood maximal operator in the Lebesgue spaces with variable exponent. The exponent function satisfies log-Holder-type local continuity condition and decay condition in infinity. The right-hand side weight to the certain power satisfies the doubling condition. Sawyer-type two-weight criteria for fractional maximal functions are derived.
  • [ X ]
    Öğe
    On a weighted inequality of Hardy type in spaces Lp(.)
    (Academic Press Inc Elsevier Science, 2009) Mamedov, Farman I.; Harman, Aziz
    The boundedness of Hardy type operator Hf (x) = integral((t is an element of R)n(:) (vertical bar t vertical bar <=vertical bar x vertical bar)) f(t)dt is studied in weighted variable exponent Lebesgue spaces L-p(.). The necessary and sufficient criterion established on the weight functions v(x), omega(x) and exponents p(x). q(x) for the Hardy operator to be bounded from L-p(.)(omega) to L-q(.)(v). The exponents satisfy a modified logarithmic condition near zero and at infinity: there exists delta > 0, there exists integral(infinity), there exists f(0) is an element of R sup(x is an element of B(o,delta)) vertical bar f(x) - f (0)vertical bar In I/W(x) < infinity: there exists N > 1 sup(x is an element of R)n(\B(0,N)) vertical bar f(x) - f(infinity)vertical bar In W(x) < infinity, where W(x) = integral({t is an element of R)n(:) (vertical bar t vertical bar <=vertical bar x vertical bar})omega(-1/(p(t)-1))(t)dt. (C) 2008 Elsevier Inc. All rights reserved.
  • [ X ]
    Öğe
    On the removability of isolated singular points for degenerating nonlinear elliptic equations
    (Pergamon-Elsevier Science Ltd, 2009) Mamedov, Farman I.; Harman, Aziz
    The well known results on the removable singularity of elliptic equations are generalized to the class of degenerating nonlinear elliptic equations. A sufficient condition for the isolated singular point to be removable has been found. in the absence of degeneration, this condition coincides with already known results. (C) 2009 Elsevier Ltd. All rights reserved.

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