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- W4384130061 abstract "<abstract><p>Let $ mathbb{S}^{n-1} $ denotes the unit sphere in $ mathbb{R}^n $ equipped with the normalized Lebesgue measure. Let $ Phi in L^r(mathbb{S}^{n-1}) $ be a homogeneous function of degree zero. The variable Marcinkiewicz fractional integral operator is defined as</p> <p><disp-formula> <label/> <tex-math id=FE1> begin{document}$ mu _{Phi} (f)(z_1) = left( int limits _0 ^ infty left|int limits _{|z_1-z_2| leq s} frac{Phi(z_1-z_2)}{|z_1-z_2|^{n-1-zeta(z_1)}}f(z_2)dz_2right|^2 frac{ds}{s^3}right)^{frac{1}{2}}. $end{document} </tex-math></disp-formula></p> <p>The Marcinkiewicz fractional operator of variable order $ zeta(z_1) $ is shown to be bounded from the grand Herz-Morrey spaces $ {Mdot{K} ^{alpha(cdot), u), theta}_{beta, p(cdot)}(mathbb{R}^n)} $ with variable exponent into the weighted space $ {Mdot{K} ^{alpha(cdot), u), theta}_{beta, rho, q(cdot)}(mathbb{R}^n)} $ where</p> <p><disp-formula> <label/> <tex-math id=FE2> begin{document}$ rho = (1+|z_1|)^{-lambda} $end{document} </tex-math></disp-formula></p> <p>and</p> <p><disp-formula> <label/> <tex-math id=FE3> begin{document}$ {1 over q(z_1)} = {1 over p(z_1)}-{zeta(z_1) over n} $end{document} </tex-math></disp-formula></p> <p>when $ p(z_1) $ is not necessarily constant at infinity.</p></abstract>" @default.
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- W4384130061 date "2023-01-01" @default.
- W4384130061 modified "2023-10-16" @default.
- W4384130061 title "Boundedness of Marcinkiewicz integral operator of variable order in grand Herz-Morrey spaces" @default.
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- W4384130061 doi "https://doi.org/10.3934/math.20231139" @default.
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