<p>We obtain the following estimate. Let <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(M_p\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>M</mi> <mi>p</mi> </msub> </math></EquationSource> </InlineEquation> be the cardinal B-spline. Then, for every locally bounded function <i>f</i><Equation ID="Equ13"> <EquationSource Format="TEX">\(\begin{aligned} \left| \sum _{k=-\infty }^\infty M_p(nx-k)f\left( \frac{k}{n}\right) -f(x)\right| \,\le \, \omega _2\left( f,\,4\,\frac{\sqrt{p}}{n},\,\left[ x-\frac{p}{2n},\,x+\frac{p}{2n}\right] \right) . \end{aligned}\)</EquationSource> <EquationSource Format="MATHML"><math display="block"> <mrow> <mtable> <mtr> <mtd columnalign="right"> <mrow> <mfenced close="|" open="|"> <munderover> <mo>∑</mo> <mrow> <mi>k</mi> <mo>=</mo> <mo>-</mo> <mi>∞</mi> </mrow> <mi>∞</mi> </munderover> <msub> <mi>M</mi> <mi>p</mi> </msub> <mrow> <mo stretchy="false">(</mo> <mi>n</mi> <mi>x</mi> <mo>-</mo> <mi>k</mi> <mo stretchy="false">)</mo> </mrow> <mi>f</mi> <mfenced close=")" open="("> <mfrac> <mi>k</mi> <mi>n</mi> </mfrac> </mfenced> <mo>-</mo> <mi>f</mi> <mrow> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> </mfenced> <mspace width="0.166667em" /> <mo>≤</mo> <mspace width="0.166667em" /> <msub> <mi>ω</mi> <mn>2</mn> </msub> <mfenced close=")" open="("> <mi>f</mi> <mo>,</mo> <mspace width="0.166667em" /> <mn>4</mn> <mspace width="0.166667em" /> <mfrac> <msqrt> <mi>p</mi> </msqrt> <mi>n</mi> </mfrac> <mo>,</mo> <mspace width="0.166667em" /> <mfenced close="]" open="["> <mi>x</mi> <mo>-</mo> <mfrac> <mi>p</mi> <mrow> <mn>2</mn> <mi>n</mi> </mrow> </mfrac> <mo>,</mo> <mspace width="0.166667em" /> <mi>x</mi> <mo>+</mo> <mfrac> <mi>p</mi> <mrow> <mn>2</mn> <mi>n</mi> </mrow> </mfrac> </mfenced> </mfenced> <mo>.</mo> </mrow> </mtd> </mtr> </mtable> </mrow> </math></EquationSource> </Equation>This result is sharp for every irrational number <i>x</i>, and the order of the step is optimal.</p>