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<p>In this article, we give condition on <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(L^p\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mi>p</mi> </msup> </math></EquationSource> </InlineEquation>-functions to form multipliers. Next, we produce similar results for product of two weighted <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(L^p\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mi>p</mi> </msup> </math></EquationSource> </InlineEquation>-functions. Thereafter, we derive new multipliers as convolution of two Sobolev space functions. After that, we study the <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(L^p\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mi>p</mi> </msup> </math></EquationSource> </InlineEquation>–<InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(L^q\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mi>q</mi> </msup> </math></EquationSource> </InlineEquation> boundedness of the operators corresponding to a variant of Bochner–Riesz multiplier. We also give a simple proof of generalised Hörmander multiplier theorem.</p>

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Some results on \(\varvec{(p,q)}\)-Fourier multipliers

  • 期刊论文

  • 发表日期：

    2026年7月18日

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  • Santanu Debnath,
  • Arup Kumar Maity

摘要

In this article, we give condition on \(L^p\) L p -functions to form multipliers. Next, we produce similar results for product of two weighted \(L^p\) L p -functions. Thereafter, we derive new multipliers as convolution of two Sobolev space functions. After that, we study the \(L^p\) L p – \(L^q\) L q boundedness of the operators corresponding to a variant of Bochner–Riesz multiplier. We also give a simple proof of generalised Hörmander multiplier theorem.