<p>This paper investigates the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({L^{p}}-{L^{q}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>L</mi> <mi>p</mi> </msup> <mo>-</mo> <msup> <mi>L</mi> <mi>q</mi> </msup> </mrow> </math></EquationSource> </InlineEquation> estimates of solutions for a class of higher-order Schrödinger equations of the form <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(u_{t}(t,x)=iP(D)u(t,x)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>u</mi> <mi>t</mi> </msub> <mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo>,</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> <mo>=</mo> <mi>i</mi> <mi>P</mi> <mrow> <mo stretchy="false">(</mo> <mi>D</mi> <mo stretchy="false">)</mo> </mrow> <mi>u</mi> <mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo>,</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>, where <i>P</i>(<i>D</i>) is a real degenerate elliptic partial differential operator. We obtain the improved global smoothing effects for the above equation, based on a global point-wise time-space estimate of the oscillatory integral <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(F^{-1} (ae^{itP} )(x)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>F</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mrow> <mo stretchy="false">(</mo> <mi>a</mi> <msup> <mi>e</mi> <mrow> <mi mathvariant="italic">itP</mi> </mrow> </msup> <mo stretchy="false">)</mo> </mrow> <mrow> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>, where <i>a</i> belongs to some symbol class and stands for the smoothing.</p>