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- W2000249265 abstract "Suppose that a bounded function <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=m> <mml:semantics> <mml:mi>m</mml:mi> <mml:annotation encoding=application/x-tex>m</mml:annotation> </mml:semantics> </mml:math> </inline-formula> satisfies a localized multiplier condition <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=sup Underscript t greater-than 0 Endscripts StartAbsoluteValue EndAbsoluteValue phi m left-parenthesis t Superscript upper P Baseline dot right-parenthesis StartAbsoluteValue EndAbsoluteValue Subscript upper M Sub Subscript p Baseline greater-than normal infinity> <mml:semantics> <mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:munder> <mml:mo movablelimits=true form=prefix>sup</mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi>t</mml:mi> <mml:mo>></mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:munder> </mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mo stretchy=false>|</mml:mo> </mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mo stretchy=false>|</mml:mo> </mml:mrow> <mml:mi>ϕ<!-- ϕ --></mml:mi> <mml:mi>m</mml:mi> <mml:mo stretchy=false>(</mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msup> <mml:mi>t</mml:mi> <mml:mi>P</mml:mi> </mml:msup> </mml:mrow> <mml:mo>⋅<!-- ⋅ --></mml:mo> <mml:mo stretchy=false>)</mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mo stretchy=false>|</mml:mo> </mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msub> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mo stretchy=false>|</mml:mo> </mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msub> <mml:mi>M</mml:mi> <mml:mi>p</mml:mi> </mml:msub> </mml:mrow> </mml:mrow> </mml:msub> </mml:mrow> <mml:mo>></mml:mo> <mml:mi mathvariant=normal>∞<!-- ∞ --></mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>{sup _{t > 0}}||phi m({t^P} cdot )|{|_{{M_p}}} > infty</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, for some bump function <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=phi> <mml:semantics> <mml:mi>ϕ<!-- ϕ --></mml:mi> <mml:annotation encoding=application/x-tex>phi</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. We show that under mild smoothness assumptions <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=m> <mml:semantics> <mml:mi>m</mml:mi> <mml:annotation encoding=application/x-tex>m</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is a Fourier multiplier in <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper L Superscript p> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msup> <mml:mi>L</mml:mi> <mml:mi>p</mml:mi> </mml:msup> </mml:mrow> <mml:annotation encoding=application/x-tex>{L^p}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. The approach uses the sharp maximal operator and Littlewood-Paley-theory. The method gives new results for lacunary maximal functions and for multipliers in Triebel-Lizorkin-spaces." @default.
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- W2000249265 date "1988-01-01" @default.
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- W2000249265 title "Some inequalities for singular convolution operators in $Lsp p$-spaces" @default.
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