scholarly journals Boundedness of fractional integrals on weighted Herz spaces with variable exponent

2016 ◽  
Vol 2016 (1) ◽  
Author(s):  
Mitsuo Izuki ◽  
Takahiro Noi
Keyword(s):  
Variable Exponent ◽  
Fractional Integrals ◽  
Herz Spaces

scholarly journals Multilinear Singular Integrals and Commutators on Herz Space with Variable Exponent

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Amjad Hussain ◽  
Guilian Gao
Keyword(s):  
Singular Integral ◽  
Variable Exponent ◽  
Singular Integrals ◽  
Sufficient Conditions ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Herz Space ◽  
Herz Spaces ◽  
Multilinear Singular Integrals

The paper establishes some sufficient conditions for the boundedness of singular integral operators and their commutators from products of variable exponent Herz spaces to variable exponent Herz spaces.

scholarly journals Higer-order commutators of parametrized Marcinkewicz integrals on Herz spaces with variable exponent

2020 ◽  
Vol 3 (1) ◽  
pp. 56-70
Author(s):  
Omer Abdalrhman ◽  
◽  
Afif Abdalmonem ◽  
Shuangping Tao ◽  
◽  
...  
Keyword(s):  
Variable Exponent ◽  
Herz Spaces

scholarly journals Variable exponent fractional integrals in the limiting case α(x)p(n) ≡ n on quasimetric measure spaces

2020 ◽  
Vol 27 (1) ◽  
pp. 157-164
Author(s):  
Stefan Samko
Keyword(s):  
Growth Condition ◽  
Lebesgue Space ◽  
Measure Space ◽  
Variable Exponent ◽  
Fractional Integrals ◽  
Variable Order ◽  
Fractional Operator ◽  
Open Set ◽  
Measure Spaces ◽  
Limiting Case

AbstractWe show that the fractional operator {I^{\alpha(\,\cdot\,)}}, of variable order on a bounded open set in Ω, in a quasimetric measure space {(X,d,\mu)} in the case {\alpha(x)p(x)\equiv n} (where n comes from the growth condition on the measure μ), is bounded from the variable exponent Lebesgue space {L^{p(\,\cdot\,)}(\Omega)} into {\mathrm{BMO}(\Omega)} under certain assumptions on {p(x)} and {\alpha(x)}.

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